Depends if I'm on the road with no other choice but to buy & use a sealant (only if a mushroom plug does not address the leak), I will. Other than that, the solution I plan on taking is to remove the tire & have it "patched". That could interfere with the beads positioning during riding but would at least let 'em (the beads) try to do their job. In fact, with the weight of the patch present inside the tire, a certain amount of the beads should find themselves on the "opposite" side of the tire during the ride to counter the patch weight.
Them beads are smarter than you might give 'em credit fer.
Also, if a sealant gets me out of a "pickle" while on the road, I'll need to purchase more beads (if they have proven to be the better approach to balancing the tires), jank the wheel off, have the tire cleaned, patched & install the beads again.
See ya.