is the balancer you replaced the other with new? It it is old, it may be bad as well.
Yes, you can pull the trans out without removint the bellhousing. That is a good time to check for round out, or rather if the center of the flywheel is at the center of the bellhousing. While you are looking, check the pilot bushing in the end of the crankshaft for out of roundness. It might give you some insight as to the lineup of the transmission.
Other things to consider are a bad input shaft bearing in the front of the transmission, causing the input shaft to be able to vibrate with a resulting shifter shake...
Good luck.