Kristi-
The way I see it, you've got a few options here:
A) Pick up the numbering system from your existing textile boxes. So if your last textile box was 20, your next created box would be 21 (or 2.1 or 2A or whatever your numbering convention is). When you transfer things from their moving box to their new archival box, I'd record the moving box number in a convenient field, just for reference. This, to me, is the easiest path.
B) If you want to make it clear that the textiles boxes are textile boxes, and everything else is works on paper/object/whatever, you could do something like keep your textile boxes with their current convention (20), but make your new storage boxes something like C01, or P01, or 1.2 1.3 1.4 (in correlation with a shelf number, if you felt so inclined). The numbering system would indicate that these are not the textiles you're looking for. The downside to this is I can see the opportunity for confusion for the next person in your position, so whatever you do, try to leave some sort of document for why you did what you did and how it continues. Also- I'd record the moving box number again. I think this could be dangerous and a potential headache, but in the right situation it could be applied.
C) Use the box number. You mentioned you're hesitant to carry over this system- what were its deficiencies? I always check myself when I am thinking about renumbering, because it increases the risk of error (36, not 63, 11 instead of 77, just out of pure exhaustion). If you've already recorded their existence in Box Whatever, and you just need to move them to a more archival container, maybe just transfer the identifier? Or use the box identifier with some modification- so Moving box number was 101, new archival box would be 101.A or A101, that way you'd be able to track which boxes have been rehoused and which remain to be opened.
When I've moved collections (more instances than I really care to think about and have conveniently blocked from my mind), I've typically tried to carry over some level of consistency. In each unique circumstance, there has been a case made for using each and every one of the three systems above- and some that I can't articulate well here. Whatever course you decide to take, make sure your decision is recorded, and if numbers are changed, they are recorded as well.
Best of luck!
Cheers,
Tracey Berg-Fulton
Registrar
August Wilson Center for African American Culture
980 Liberty Ave.
Pittsburgh, PA 15222
Ph. 412-338-8737
F. 412-258-2701