You might also be able to defer your membership to the union for one show. Under the Taft-Hartley act (also known as the Labor-Management Relations Act), a person may defer membership to a union for a specific trial period. In the case of AEA, it's one production. Contact the membership department at AEA for more specific information. An SM at the company I work with exercised this option. She signed an AEA contract, but she struck clause 7, the clause regarding membership/the deduction of working dues. She was paid at the standard SM rate, but no dues were deducted. The company still paid all Equity benefits (pension, health, etc) despite the deferment.
It's definitely worth investigating if you really want the job but aren't quite ready to go union.
People do that in PA because it's a Right to Work state, so you can't require people to join a union to do union work, though I know of people who have taken advantage of that and do it continually.
Just be careful about it.
Personally, and it's really only my opinion, I don't think you should take a union job unless you're willing to be a part of that union, which includes paying the dues and the initiation (which i really what everyone is referring to here, I think, because it's $1000- or did it go up to $1100??). The people at Equity aren't some horrible monsters, and if you know that it's a step you want to take, but can't afford to pay, talk to them. I had an actor on an SPT 1 contract who was only getting paid $125 a week, and was in between part time jobs, so it was his only income for a while. He talked to AEA, explained the situation and they were more than willing to allow him to stop paying for the duration of the show.
Only take the step if you're ready to. If scheduling is the problem, talk to the PM and the SM if you can. Maybe they know the rehearsal schedule and you can miss an hour or a night at the beginning of the process. If there's a PA as well, it may not be a problem.
It took me 4 years of working in the same place to feel that I was able to ask to miss a show to go to my sister's graduation, but it was fine. I trained some one, and shadowed them while they ran the show twice and then they were on their own for 2 days. People have lives and other responsibilities in those lives, and as hard as it is to believe, you're allowed to. If you have other work opportunities that have been scheduled, see if you can work it out, if the ASM job is what you want to do.