This is such a common dilemma. A friend of mine solved it by having a separate celebration after the actual wedding at a restaurant with those they could not afford to invite to the wedding itself.

They sent out the invites and stated that each had to buy their own dinner, but they purchased a few bottles of wine for the tables.

It was a good idea, and those they couldn't invite were happy they were still able to celebrate with them. The fact that guests had to pay for their own meals didn't seem to be an issue at all.

Another idea could be to host a small byob at your home before or after the wedding. It would be quite inexpensive as you're only really buying some munchies or finger foods and everyone feels like they are a part of your wedding.