As to your specific situation on being stuck on a crucial point, I would stick the whole thing in the drawer for a few months and play with something else. You might find that the perfect solution comes out of the blue or in a re-read later realize that yet another major rewrite needs to be done. In fact, you may never come back to this story and end up canabalizing it to incorporate sections and scenes into another work. That isn't a bad option either.
Several times I start a work thinking I have the most unique and fascinating premise, but, in the details, it just implodes on me. Luckily, after experiencing this the hard way several times, it happens less and less.
Keep your hopper full and your head above water. Putting it away in that drawer to 'ripen' or to 'spoil' is far better than investing countless hours in something that simply refuses to work effectively. Not all stories are meant to be told at this point in time.
Best wishes and a virtual hug to this writing friend and to others in search of stuffing their writer's toolbox.