my cousin did this, he and his wife got married in Vegas this was a second wedding for her but anyways they had a back yard bbq that was sooo much fun!! we had food, cake, and a dj! honestly do what makes you happy!
The reception is a celebration of a marriage, not just a way to thank people for coming to a wedding. Just because you choose to do a DW and choose not to invite everybody (many would probably not be able to go anyway), does not mean you and your marriage don't deserve to be celebrated. Go for it! Surely there will be some people that understand and will be happy to attend, and others that think it is wrong. But even if you did the ceremony and reception in a traditional manner, certain personality types will always find something to whine about in terms of how you do your wedding. It is Your special day, not theirs- do it how you want. And when it comes to gifts, many people will still want to give you something. This can get tricky, but I would just let people ask the host where you are registered. This way people don't feel obligated, but IMHO people who want to give you a gift will, and people who don't want to won't.
I think that you should do whatever you want to do and if that is more affordable for you then I say go for it no matter what anyone thinks or says, because it is your day NOT THEIRS and it is one day that is all about you. They can have opinion but they dont have the right to tell you what to do for your wedding. They can save their ideas for their own wedding. My fiance and I are planning something similiar to what you guys have, expect ours is still going to be in the city but down by the river in the middle of august and we are only inviting close family and friends and then the reception is something that everyone can be invited to. But dont let anything that anyone tells you make you think that you have to plan your day a certain way to please everyone else. The only people it should really be pleasing is you and your fiance.