Welcome aboard!!

Personally, the best advice I can give is "get used to it".  I.e. the feel of both types of sticks.  It's all about using the right tool for the job.  I think the more you switch back and forth between gigs and stick requirements, the more you will get used to them--and thus the control needed with each.

Congrats on being in such a diverse drumming situation.
Nice work.

A quick way to fool your hands into thinking the 5Bs are more hefty is to do this:

After playing with the fife-band sticks, but before picking up the 5Bs, grab a pair of 7As or something similar, and go through some patterns and routines with them until they start feeling like sticks as opposed to toothpicks. Then pick up the 5Bs, which I bet will feel much more substantial by comparison.

I went through this when I was in the marching band at Indiana University, and that's the trick I came up with for making the transition between big sticks and little ones in the course of the same afternoon.

All good tips, especially the one about warming up with 7A's for awhile.  Thank you all.