Learning how to bar is tricky! My suggestion is to concentrate on the Bbm7 shape . . . 1111 . . . Yep, bar the open strings and nothing else.
Hmmmm... One of my students wanted us to learn the song
Red Swan/Attack on Titan Theme with this Bbm7 chord... and here is what I found:
It was quite easy to play on some of my ukes, and almost impossible on others... depending on neck thickness and how the transition of the neck to head-stock is shaped.
My Kala Travel Tenor has a very thin neck and the "bump" that is formed by the radius change at the transition point is very small... makes playing this chord pretty easy...
My Pono tenor has a really fat neck to accommodate the truss rod, making it almost impossible to barre at the first fret. I ended up taking a rasp and changing the neck to head-stock transition/profile on the 'downhill' or underside of the neck, and then sanding it back to polish. I took away quite a bit of wood here, but I can play that chord with no problem now.
I ended up doing the exact same thing to my Fluke Tenor, for the exact same reason. That single open slot(?) head-stock is cool looking - but quite wide and it really gets in the way of the Bbm7 chord being played. A quick trip out to the garage and a few minutes with my trusty Shinto saw rasp made this job easy. Then just sand and polish back up to 3000 grit using a standard course of sand paper... and then I'm playing 1111 with ease.
My Bruce Wei has a different issue: The A string tuner is in the way! I develop a tiny blister after playing that song a couple of times in a row because the base of my pointer finger rubs against the hold down screw and gear wheel. Not sure how to fix that, but changing out those open back Der Jung tuners might be in my future. Not sure what brand will accomplish this yet... so I avoid playing that song on this ukulele!
My Pono Baritone is older and has a different neck profile, so I can barre this chord shape just fine. (It's now an Fm7 or something... but it works.)
I never even thought this would be an issue until I fell in love with this song...
But in general: I cheat when playing barre chords: I lay down my middle finger and then place my pointer finger on top of it for extra hold down power... I find this especially helpful when playing "fake" E (4444).
I teach my students this as well, since kids have a hard time keeping all the strings down at once. It's a bit inefficient, but it works!