My AMA chartered club has been in existence since the 60's. The original founding individuals actually went through the steps to register as a club with the state. That data hasn't been updated since the early 70's but the state still lists us as out there. But since that time the succeeding administrations haven't bothered with that 'stuff'.
Fortunately, no one has been seriously hurt on our field in all those years. What few cars that have been smacked by planes have been handled by the AMA umbrella coverage.
Couple of things to keep in mind:
Not-for-profit (NFP). A LOT of people have the odd notion that the 'club' can't have a 'profit' at the end of the year. They think the bank balance a the end of the year has to be zero. And they'll get in your face serious about that. As you've found out, it is an IRS term and an IRS term only. It is difficult to qualify and maintain the paperwork as an educational NFP, the end purpose it to not have to pay taxes on sizable income, and make sure that when the club folds up, any money in the treasury and real property are given to another qualified NFP (i.e. the AMA) If you divide the remaining funds of the club back to the remaining members then you have just 'profited' from the club and are now responsible for all the taxes you haven't been paying as an NFP.
Money: Have a set of double checks and balances on your club's funds. We had a treasurer who read our by laws that the 'officers' could spend up to $500.00 per month without a vote of the membership. So he'd use his landscaping companies equipment, haul in a load of gravel to the parking lot or dirt into some holes in the field and pay HIMSELF $500.00 out of the treasury. When he got called on it he, thankfully, left. Get co signed checks, or a written vote of your board on ANY expenditures of ANY amount.
Do have a written set of bylaws as to the responsibility of the club members and officers and do have a written set to club safety standards that apply at your field. When I first joined my club in the 90's there was continual wailing and gnashing of teeth with members constantly bashing one another with club 'rules' violations. At my second or third meeting I asked what were these 'rules'. I got a "Everyone in this club knows the rules!" shout-down from one of the oldest members and biggest basher. I replied with I'm a member, and I don't know the rules and if you can't show me them in writing, then they don't exist. Guess what? 90% of what this guy was using to spoil the fun of the entire club were things he'd made up in his head and they changed from month to month. A one-page written set of field operations rules that's maintained, and everyone gets a copy when they renew their membership keeps this kind of nastiness to an absolute minimum. My club's been a pretty nice place since we put everything in writing. I'll pm you copies if you'd like.
Best of luck.