Don't make much BHO anymore but when I did, I found the biggest effect on my yield was, as someone else already stated, the quality of the product going in. I expect 20% returns from top quality bud-only, kept as intact as possible (whole buds) and loosely filled into the tube. I want the consistency of the material in the tube to be "spongy" if that makes sense.
It should feel like you could still pack a decent amount of material into the tube if you packed it down, but don't do this. You also don't want it to feel loose. You definitely should be able to shake the plant material around inside the tube.
This, in my experience, maximizes both yield and quality, and should easily let you average 10% returns with a decent quality trim/bud mix.
Minimal liquid butane contact with plant matter means fewer impurities extracted, so you want to minimize the amount of time the butane spends inside the tube and minimize the surface area of the plant matter.
Also, packing the tube too tight is, of course, what causes the butane to evaporate while still in the tube and completely killing your yields.
Most of the Cannabinoids are in the trichomes are on the surface of the plant anyway, so don't bother grinding it up finely.
Also, I find that using a fine stainless steel micron mesh has a noticeable effect on yield over coffee filters, so you're definitely on the right track with that. I've never personally tried silkscreen, seems like it could be a finer material without being absorptive like paper coffee filters. Either way, I cant see the screen size making that much of a difference. The screen is really there to stop plant matter from going through. The trichomes are all dissolved in the liquid butane - or at least, should be dissolved in the liquid butane.