You’re not stuck! You’ve just let your company make you believe that you’re stuck.
Right now, this is all your problem because you’ve agreed — through your actions rather than your words — to make it your problem. Your managers don’t have an incentive to find real solutions because your apparent willingness to continue being overworked is their solution. (To be clear, if they were decent people or decent managers, their incentive would be that this is horrible and unsustainable for you. But apparently that’s not a concern for them.)
You said you can’t let work drop because it could affect the organization’s future funding. But if your management cared about that as much as you do, they would be putting other plans in place, like hiring additional staff to replace people who leave. They’re not doing those things, so right now you’re operating as if you care more about keeping the organization afloat than your employer does, no matter what the personal cost to you.
I think it will help immensely if you can get clearer in your own mind about what your responsibilities are versus what management’s are. Your job is to clearly explain what you can and can’t get done in a reasonable and sustainable amount of time. Their job is to decide what to do about the rest of it, whether it’s hiring more staff, dropping clients, cutting down on work, or whatever other solution they settle on.
Your part sounds like this: “I was willing to help out in the short-term when we were in a pinch after Jane left, but I’ve been working 11-hour days and it’s starting to affect my health. I need to return to my normal hours, which means that I will be able to do X, Y, and Z, but not A, B, and C.”
You will also need to be prepared to say things like this (both in this initial conversation and going forward if/when they try to pile more work on you):
“I can do that this week, but it means X won’t get done.”
“I want to remind you that we agreed I wouldn’t focus on X because you needed me to prioritize Y.”
“To make sure we’re all on the same page, I will focus on X for the next week, which means that I won’t be working on Y and Z.”
“X hasn’t been done at all this month and I won’t be able to do it anytime soon. I want to flag it in case you want to bring someone else in to handle it.”
“I can do X and Y, or X and Z, but not all three. My plan is to do X and as much of Y as I can get through by the 20th. Let me know if you want me to prioritize them differently.”
If you don’t set boundaries and instead try to get everything done, no matter what impact it has on your quality of life (like your sleep, or your health), you’re taking on the full burden and ensuring that your employer won’t feel the problem personally. You keep telling them it’s unsustainable, but then you do the work anyway, so from their perspective, everything is getting handled and there’s nothing they need to change. It’s working fine for them! (Again, a good manager would still intervene because this is a crappy thing to do to someone. But you clearly don’t have good managers.)
That means you need to be less invested in keeping your office running smoothly, and more invested in defending your own boundaries. It doesn’t make sense for you to be more committed to the company’s functioning than your management is, and if they were as committed as you, they would be acting on all the alarms you’ve been sending up. They’re not, so you don’t need to be either. This isn’t your company and you don’t need to run yourself into the ground to keep it afloat. Work your eight hours — work an occasional nine if you really feel like it — and then go home. You’re selling your labor during a reasonable workday; you’ve haven’t sold the rights to all your waking hours.
Because this is a change, you should give your managers a heads-up in advance: “Next week, we have patients scheduled between 7 a.m. and 6 p.m. I can’t keep working 11-hour days, so I can handle the ones scheduled from 9 a.m. to 5 p.m., but someone else will need to cover the appointments before and after that.” If they push you to cover it all, say, “I’m not able to. I was able to pitch in for a while, but I’m not available for 11-hour days anymore. For the sake of my health, I need to return to the eight-hour day I was hired for.” The key, though, is that from then on you need to be willing to let the chips fall where they may, so that someone other than you feels the pain of the situation. Because you’re conscientious, you’re probably going to struggle with doing that, but it’s the only way your unrealistic workload is going to be solved.