Wow, 1000 names in 16" doesn't give you much room to work with. Who's going to do the spell check on those names? I would tell them to do it themselves... You can go down to a 4 pt font but you will need a very high mesh count like in the 300+ if you can even find one like that. Ryonet has 305 mesh, but you'd need higher than that. Some people are very unrealistic. How many handkerchiefs do they want? The problem is that with sublimation the letters would get lost in the fabric. With screen printing you might not lose the fonts in the fabric but you will lose them in the emulsion and in the screen itself. With sublimation you could also put a design in the background in color. I just can't see fitting 1,000 names on it.. I don't think they would be readable. You could try heat transfers too. Are they supplying the hanky? You might even be better off with DTG. I think screen printing might be pushing it. Don't know. I've never tried to print anything that small.