I've been using the JMJ exclusively for about 6 months (roughly 40 gigs and weekly rehearsals). I prefer a tension that is close to strings I use on 34" scale. Note that I'm not all that picky about strings, although my favorites are Rotosound RS66 and Chromes.
I ended up with Rotosound RS66LE (50-70-85-110) as my current go-to. This is a long-scale set and getting the .110 E wrapped on the post takes a little extra effort, but it works. I play in 2 bands. One is mostly "Outlaw Country" and the other is mostly "Classic Rock". I need to tune the E to "drop D" on several tunes so the .110 E is my current preference when using round wound strings.
My favorite in the FOH mix were the Chromes. The tension on the E (.100) and A (.80) were a bit low for me. I'll be trying a custom long-scale set, probably 45-65-85-105 (or 110) in the near future. If I can get a fatter flat wound E on the post, I'll be very happy.
These are strings I tried that I could gig with: Boomer Medium Scale (45-65-85-105), GHS Super Steels Medium Scale (44-63-84-106), La Bella MUS.
These are strings I tried that I couldn't gig with: D'ddario 170 BT (45-60-80-107) due to low tension on A and D strings, Rotosound RS77M (40-50-75-90) due to very low tension on all strings.
Obviously, YMMV. Best of luck finding what works for you. The good thing is the JMJ is string through so there are long-scale sets that can work, broadening your choices.