One fix may be to try my new favorite strings-DR Tite-Fit. You didn't mention your preferred gauge or what the JS was strung with, but as a lifelong 10's user I have been able to go to 11's and even 12's on my LP's without a noticeable difference in feel. So if you use 9's for example, try a set of DR Tite Fit 9's and that will give you a looser feel. The difference has to do with the way the strings are wound on the cores, although the plain strings will feel almost the same. You can't even believe the sound of a
les paul with 12's, YEE HA! *Z