My sympathies for your plight. Based on my own experience I can tell you this:. They will not under any circumstances disrupt any other flights to fix yours. IF they can round up another aircraft within a few hours they might, but only if they don't need it somewhere else. If it is smaller than yours, there will be a scramble to sort out who goes and who doesn't. I haven't seen any evidence of a rational procedure or priority in this circumstance.
The most likely outcome is they will cancel outright and rebook you on later flights if and when there's room. Again, priority seems to go to those who get to an agent first, either in person or on the phone.
Some will say that the rebooking is "automatic" and that status matters, but again, my experience is that this is at best a crap shoot.
Good luck. Let us know how it goes.