This looks deceptively easy to fix. An experienced person could do it with little trouble. Have to remove tuners (as you said), remove any loose splinters in the break, and line it up. Be sure it fits together perfectly. I'd use wood glue, but if Beau or Ken tell you epoxy, that's great. It is really the right choice, but I don't use it where it will come in contact with the finish.
If it was me, I'd disassemble the tuner assembly on the string#1 side and re-mount just the gang-plate. Using the screws will help you keep the glue joint aligned on that side. (You may need a longer screw to replace the one closest the nut, because the hole's been stripped out.) Too bad the string#8 side doesn't have this advantage. Without said advantage, I would line it all up, with the one gang-plate with all screws installed, and drill from the back, somewhere near the center of the break at the other (string#8) side of the headstock. Not all the way through (save the front) using a bit just the right size to slide in a small brad or nail. Now I'd have a way to keep my glue joint from sliding during clamping and glue-drying. Remove the screw, apply the glue, align the broken parts, re-install the screw, lube the brad with vaseline and insert it into the hole, and clamp (clean up squeeze-out as needed). After appropriate drying time, remove the clamps, pull the brad out, remove the tuner gang-plate, and re-assemble. After stringing it up, I might do some bit of filling and finish repair on the little hole in the back, but probably not, because I would probably be throwing the ukulele in the garbage and kicking myself for not taking it to a professional. (and I've done hundreds of these sort of repairs.)