Looking at Great Tapestries edited by J. Jobe (1965) and the section in the back by the professional tapestry weavers Francois Tabard and Jacques Brachet, entitled, The Weaver's Art, we see that Tabard (and Aubusson by extension) do not feel that handspun has sufficient uniformity to be suitable for tapestries. That is silly. Many of our finest tapestries were woven before mill spun. Their existence is proof that a competent spinner can produce yarn suitable for a fine tapestry.
What Tabard meant is, "Contemporary hand spinners do not generally produce high quality yarn." In particular, he is talking about uniformity. This is in contrast to Verlet's and Florissone's themes that in the Gothic and Classical periods, hand spun yarns produced fine tapestries.
Tabard tells us that 2/20 yarns (2-ply at ~5,000 ypp) is fine enough for almost any tapestry. (One must stand back to see all of a big tapestry, and at a few steps back, 2/20 yarns provide a higher resolution than the human eye can see.) That is about the grist of the commercial mill spun warp that I buy. The French, Italian and English tapestries that I enjoyed in Paris were woven (and restored) with yarns of about that grist. However, the 16th century Flanders tapestries were woven from finer yarns. They even look good when you get so close that the guard is running toward you, shouting for you to get away from the tapestry. I was not touching it! Really!!
I suggest to you that if you having trouble with uniformity, spin finer - and use coarser wool. The advantage of spinning wool at the wool's spin count is that the single, and hence the yarn will be very uniform. Let me say that again: spinning wool at its spin count ensures a uniform yarn. I'm pretty sure that (some) of those very fine tapestries from Flanders in the first half of the 16th century were woven from 2/40 (2 ply at ~10,000 ypp/ e.g., singles of 40 meters/gram) which was plied from a standard grist of single that spinners in Flanders were producing for shirting. They used DRS spinning wheels set to insert 15 tpi which results in worsted singles of about 18,000 ypp. (Right now, my spinning wheel is set to insert 17 tpi resulting in worsted single that is very close to 22,400 ypp. I assure you that such singles can be spun at a rate of 2,500 yards per day on a sustained basis.)
Those singles were in the range of 32s to 40s (e.g., 40 hanks of 560 yards each per pound). Spun from coarse long wool such as Cotswold, the thread is very lustrous, strong, and durable. 40s are more lustrous than 20s spun from the same wool. However, spinning these long wools finer, (e.g.,44s) is more effort. And, in a time when rooms were lit only by fire, more lustrous wall hangings were much more valuable. That is, my thoughts about grist are driven by a compromise between spinning effort and the need for luster. (Mill spun does NOT provide that luster. See http://awordfromclaudia.mirrixlooms.com/2011/01/tapestry-yarn.html, http://finefiberpress.blogspot.com/ , https://www.etsy.com/shop/FineFiberPress , http://members.peak.org/~spark/FineFiberPressTapestryYarns.html OK,! it is worsted spun from combed fiber, but different breeds have different luster, and higher grist shows the luster off better. The AVL from Fine Fiber is ~3,200 ypp.)
Francois Tabard and Jacques Brachet simple got it wrong. I find this funny as the Apocalypse Tapestry (http://en.wikipedia.org/wiki/Apocalypse_Tapestry) is genneraly considered to have been a major artistic influence on both Tabard and Lucrat (another great weaver) in the 1930s. In the old days, hand spinners did spin yarns for high quality tapestries, because mill spun did not exist. Was the warp as uniform as modern mill spun? NO! However, the long wool was stronger and more durable. And, the hand spun weft was adequately uniform considering the acuity of the human eye. Using mill spun, modern weavers never get the full luster of worsted spun long wool.
Tabard and Brachet were correct in that contemporary (1965) spinners using typical modern hand spinning tools are not likely to produce useful amounts of 2/20 worsted yarns with the necessary consistency. Tabard and Brachet had never worked with high luster yarns, so luster was not something that they expected pr thought about in their yarns.
Hand spinning can produce better yarns for tapestries than mill spun, and can produce those yarns in useful quantities. Standing back a few feet means that a small lack of uniformity in the yarn does not diminish the over-all effect for the human eye. It is the same issue that says 2/20 is a fine enough yarn. And, the hand spinner can work with lustrous long wool, or silk, or rayon, or nylon, or silver /gold/ aluminized mylar fibers, or even polyester. You can even make transparent yarns. However, use of DRS controlled flyer/bobbins allows hand spinning of more consistent singles at rates 3 to 8 times faster than is possible using typical modern hand spinning tools (spindles, or single drive wheels, or double drive wheels not using DRS ). That 3 to 8 times faster is worth while because it allows more interesting projects to be completed.
For something like the Apocalypse Tapestry, the weaver would be working at something like 13 or 14 epi using a final yarn of about 800 ypp. For ease of producing a highly uniform weft yarn, I would use 6 strands of 2-ply 5,000 ypp yarn. (e.g., singles would be 10,000 ypp, e.g., ~20 hanks per pound) The 6 strands would be wound together on the bobbin but would have very little cable twist so the 6 strands of 2-ply weft (12 strands total) would lie flat on the warp and give perfect fill. I expect that about just under half a million yards of of warp and just over half a million yards of weft would be needed. It comes out to just under over 7,000,000 yards of singles.
This is a luxury project, and the use of finer singles vastly improves the look and luster of the fabric, but the additional effort to spin the finer singles is not significant. (Compared to 72 man-years of weaving!) So, while I have not seen the tapestry in person and have not seen a discussion of the yarn construction details, I very much suspect that they used what most modern hand spinners would consider ridiculously fine singles.
Weaving time for the Apocalypse Tapestry has been estimated at between 50 and 85 man-years, but it was completed in only 5 calendar years, so there were about a dozen weavers.
However, using DRS, a team of 4 spinners could easily have spun all the needed yarn (including 12-strand weft) in about 3 years. If the spinners start a few weeks before the weavers, they can have warp for 3 looms and a small stock of weft ready for the weavers. Using DRS spinning technology, a team of 30 workers could have produced the Apocalypse Tapestry in about the 5 years history says it took to make the object. The core team would have been a dozen weavers, 4 spinners, a wool comber, a dyer, assistants for handling yarn and setting up/adjusting the looms, an artist doing the cartoons and setting color palettes, a manager, and a book keeper. In the last 2 years of the project, finishing tasks would have replaced spinning tasks.
Spinning effort with spindles would have been 2 or 3 times greater. (e.g., 12 spinners) Certainly not much in the greater scheme of things, but I think that the consistency of the weft argues for it having been spun by a smaller group of spinners working with DRS wheels.
The dealer that arranged the Apocalypse Tapestry commission arranged commissions for 254 other tapestries. And, there was routine textile weaving going on nearby. Thus, there would have been continuous work for spinners, weavers, and finishers. This was weaving on an industrial scale. These were not women spinning for the needs of their family. These were not even folks spinning under the direction of their lady for local needs. These were folks in Paris making tapestries for a castle that was 200 miles away. The tapestry for the choir stalls in Tournais was woven in Arras, 40 miles away. It was 8 feet high and 65 feet long. We know there were other larger and more famous tapestry weavers closer. Thus, we can infer that textiles was a large and competitive industry. This does not fit into any of the modern mythology of hand spinning.
These were folks that knew how to get textiles DONE! Full time, professional textile workers in the time of Chaucer. You can pick at my estimates on the number and amount of singles produced, but first you need to look at the Apocalypse Tapestry and think about how you would produce that volume of yarn, of that quality, in that time frame.
The bottom line is that if you want beautiful tapestry yarn, get some Cotswold, and spin it fine.