Yeah, they're completely walking all over you, and it's obviously hurting you in more ways than emotionally.
The fact that you are considering continuing working essentially 30 hours a week for what you're getting in return for the remainder of the year - well, to be blunt that's foolish.
The fact that they've paid for professionals to do work, then given you the same work for free should cast this whole situation in a different light.
Yes, it's good to volunteer for a good organization. Yes, you may be wiling to donate services and that's uplifting and fulfilling for you.
But they are clearly abusing you. They will take and take and take and ask and ask and ask and demand and demand and demand - because it works. Then when you say no they will turn it back on you, as that person asking for a check did, blaming you for something that has absolutely nothing to do with you or your efforts, and in fact without you they simply wouldn't have it at all.
This is a business.
It's a business.
They may be doing good, but it's a business.
I'd strongly suggest divorcing the emotional/empathetic aspect of why you're doing from what you're doing and re-negotiate.
And your opening salvo isn't bad - submit your resignation effective at the end of the year. But it's not nearly strong enough, and absolutely nothing will change between now and then. And if they get a huge fee that's not your fault. Not only that but they've got over three months to solve that problem if it happens to be important to them.
The fact that they put up with a bad accountant before you should help you understand that it really doesn't matter to them, and they're just using as much of you as they can convince you to give them without regard to you.
You're a tool - an object - the organization and the people within it it uses, and it's clear form the way they are treating you and letting others treat you that they don't value you, just the work you're doing.
If nothing else, you should at least get paid commensurate with the work you're doing.
You really need to stop working after 5 hours a week, and make them understand what isn't being done, and if you're willing and able to work more, perhaps up to 30 hours but you must be paid more, perhaps up to 6 times whatever you're getting.
You have to be hard nosed about this, draw a line in the sand, and let the chips fall where they may.
The most likely outcome is that they'll relent at least a little bit, and they'll continue to badger you for more free time, but at least in this case you're getting paid more for the work you're doing.
You've got them over a barrel and you can show them exactly how much you are making/saving them a month, so you should be able to make the case that your additional paid hours will yield significant benefits for them that would pay for those hours. Point out the huge fees they're facing without a competent accountant, and how you can and have been save them all that money.
You're being far too nice. I can understand 10 hours a week to a good cause for reduce or no pay, but 30 hours a week is no volunteer position.
Your anger is completely valid, and this is no way to live. Renegotiate the terms and either cut your hours, explaining what that means in terms of money lost, or increase your pay, or somewhere in between.
This isn't good for you, and waiting even weeks, nevermind months, to resolve this issue is self-destructive behavior. Don't be a martyr - fix the problem or walk away. If you're willing to spend your emotional energy on something I expect there are groups who deserve it more than this one.
If, on the off chance, you depend somewhat on the pay or benefits of this position, then you should immediately cut your hours down to the minimum required, and report each week on the things not getting done and the money lost due to those things, and let them know you are available for more but a commensurate increase in benefits/pay is required. I've written the above assuming you're largely a volunteer, providing professional services at well below market rate for a good cause, but if you depend on this in any way then you should immediately formalize the relationship and make sure that it's completely a business relationship, rather than volunteer.
And deflect, deflect, deflect. "I cannot spend time chasing down those receipts or getting the check signed, please call [boss, president, ceo, someone else] and ask them to drive around or come to my house if this is urgent." Make sure every time someone tries to pressure you into going beyond your job requirements they are redirected to the people above you. If you receive direction from them to add that to your job list, make sure they understand the cost - hopefully in dollars and cents - of the increased time and pay and/or what will go undone as a result of these distractions from your primary responsibilities. When I've been in the position of handing out checks I simply gave the unsigned checks to the person that needed to sign them, and redirected all inquiries to them. Let them deliver the checks if it's important to the business. Note that I didn't actually give them to the person - I put them in their box in their locked office with one signature and then it was out of my hands.
If at all possible, convince them to give you a paid intern to assist you - not just with the running around, but also to help you get around for meetings and on-site work. (I can't believe they aren't paying for a building with a working elevator, and haven't moved the meetings to a better location that doesn't require stairs for you).
You deserve better.
/rant