I think it's the same scenario. You host the party you can afford.
If you can only afford drinks, then host a drinks party. If you chose to host it somewhere which also provides food you can invite people to a drinks party and let them know that the venue also offers food so they will be able to order food for themselves if they wish, but if I were asked to pay $30 per head for an engagement party (or wedding reception,or adults birthday party) it would bug me in the same way and for the same reasons as if I/my child were asked to pay $30 to attend a friend's party.
(I haven't been to many engagement parties, but those I have been to have all been either very small (a meal at a restaurant, hosted and paid for by the engaged couple, for very close friends and family) or larger but more informal (Party at someone's home, with drinks and nibbles provided by the engaged couple as hosts, (and on one occasion by their parents) or very informal (drinks in a pub one evening, first couple of rounds paid for by the engaged couple)