Transmission not shifting into second fully

That sure does sound like a linkage bind.
Separate the linkage from the trans again and see if the shifter moves through all ranges while it is disconnected.
If it seems fine then do the same thing with the linkage arm on the tranmission.

The only other thing that could physically cause that would be a WAY too tight front band adjustment.

So,,,,,is it binding up in the linkage causing it to be between 1st and 2nd or the front band?