Batspeed is not completely exit velocity. It is also the ability to have quick hands. Sometimes older players get pull happy when they lose batspeed because that is a way to swing harder. Guess right on a pitch and swing hard.
A better approach is to swing less hard but make more consistent contact. This is what Bryce seems to be doing. His sweet spot percent is tied for his career high as far back as the advanced stats go and his barrel percent is also high. This results in hitting the ball harder with a more controlled swing. His launch angle is down also.
I think the back issues (and maybe the shifts) have forced Bryce to change his swing. Remember the high K percent worries of a year or two ago? He has always been his own coach too along with his Dad. And given that most others on the team have not changed or improved, this really feels like something Bryce did and not Girardi's coaching staff (which may be giving decent advice to other players, it is just hard to tell how different their advice and success is from Kapler's staff).