I've played a few different Bigsby equipped guitars, and I've noticed that the depth of the vibrato can vary quite a bit from unit to unit. Is there a way to set up Bisbys to offer more/less depth?

Well there are different models of Bigsbys - the ones on carved/arch tops have more travel so they go deeper...

but on something like an SG or Tele, (a flat top) they have less room to detune.....

they are much more fun on an Archtop