3 pages and no one's mentioned this...
Change your strings.
Strings are constructed differently, which makes their tensility (the amount of pressure required to bring them to pitch) different. I went through this discussion when I wanted a 34" scale bass with a tight low B. I was told this can be done, but a 35" scale would give me a tighter B with a wider variety of strings.
SIT strings are made so that the low "B" is not floppy on a 34 inch scale instrument. But put DRs or D'Addarios on them and the low "B" exhibits "floppiness." I LOVE DR Black Beauties on my 35" scale - but I hesitate to put them on my 34. If only SIT made a coated string.
The construction/tightness of the neck joint has an effect on the tightness of the string as well, but I couldn't believe the truth in the brand of string argument until I tried it on my own.
Z