Well, in terms of social obligations, you are obligated to invite anyone whom your fiance asked addresses for. They are expecting a save-the-date, and save-the-dates mean you’re invited. They all will be expecting official invites. If you ask them for their addresses and it is specifically for the wedding, then you have invited them.
Given the unusual and rather extreme situation, you may nonetheless be justified in de-inviting them. It is the nuclear option, but this may be a nuclear situation. Mind you, you’ll both look like jackasses (even if the fiance does the dirty work), but the additional costs may be on a scale where you have no choice. By the sound of it, it could be a couple thousand dollars extra (depending on the venue and specific ammenities).
As far as tiered-invitations go, that is also a big no-no in the states (especially if it means some people have a huge gap of time between the ceremony and reception). I think if I was invited to a wedding where I was invited just to dance after (or to a ceremony, then a dance after everyone else had dinner, I think my response would be along these lines:
“Thank you for the invite, but I have plans.”
“Oh, okay. What are they?”
“I don’t know; I still need to make them…”
If at all possible, your best bet is to figure out a way to cut costs (or make a little extra money) so that you can afford to host the wedding for all people invited (intentionally or otherwise). Avoiding the hurt feelings and inevitable gossip will be worth having sheet cakes, no centerpieces, cheaper food, etc.
If it just can’t be done, and your only options are a tiered reception or de-inviting the mistakes, I cannot tell you which is worse.
– If you have the tiered wedding, everyone will think that you simply thought that was okay and don’t value them enough to invite them to the real thing. While this technically may be true for the mistakes (who you didn’t plan on inviting at all), if you have to inlude any other friends in the bottom tier, they will also quite possibly be at least a little offended. On the other hand, at least no one was told their invite was a mistake.
– If you do de-invite people, it will be a bigger kick to the stomach for those de-invited. However, it will not spill over into your real friends in the same way. Also, you can mitigate it by just being really upfront with them. Your boyfriend didn’t know what a save-the-date was, they weren’t meant to be on the guestlist, a lot of people were accidentally included (not just the individual you are addressing), and if you were to invite them all, it would cost you thousands of dollars that you do not have. As tacky as mentioning money can be, how much worse would it be if you don’t mention the part about lots of people and thousands of dollars, and in their minds, they think you are just de-inviting them to save $50 or however much it is per person?
Either way, tiered weddings or de-inviting the mistakes will cause a lot of problems, so only do it if there really aren’t any other options.