transmission vibrates when shifting into drive

I think these guys are right.
It may not be a vibration your feeling, it may be a forward clutch chatter in the trans on application.
If you can do a line pressure test or take it to a shop that can do it for you (any trans shop can) then that would be a great tell tale.
Things inside transmissions don't get out of balance until right before it explodes and yours still drives.
Look up the line pressure specs and if it's low beyond specs then it's time for it to pulled for an inspection to find out where the pressure loss is.
If it still drives but has low pressure it's almost always pump or governor sealing rings.
This isn't an oppinon, it's experience.
Here's hoping it's an easy fix for ya.