If I received an invitation to a friends' commitment ceremony, yes I would attend. It doesn't matter whether it's a commitment ceremony or a wedding. A wedding is exactly that, a commitment ceremony, but usually with the flash dress, flowers etc.

Remember who's day it is. It's yours and Shel's. No-one else's. If you think you're doing it on the cheap, then changed your plans a little. If you're happy with your plans, then keep them.
IMO, I don't think what you're doing looks cheap. You want it to be a casual, intimate affair. So asking your guests to buy their own dinner fits in well with that theme.

Most weddings you go to only offer beer, wine & softdrink anyway. As yours is only a small, casual dinner, than to not offer alcohol is fine. Having a champagne toast will certainly bring special meaning to it.