I’d remove the machine head/tuners on the bad side too. There will probably be a nut on the other side that you can undo and the tuners will just pull through. That will give you more working room and allow you to get the glue along the whole crack.
I’m less sure about this one but you could, very carefully slide something like a knife to open the crack out a little. The is might allow the glue to flow in better. If your glue is runny, it might not make that much of an improvement, so perhaps not worth risking cracking it off completely. (Although the glue will be plenty strong enough, if you take off the broken part it might not be easy to line it back up properly. If it’s still attached, you’ll be right.)
FWIW I once cycled 3 miles home with a new guitar too. It was in a heavy flight case and I thought it would be fine to carry it under one arm and wobble back one handed.