I eloped - I was in an immigration situation, and having a big wedding was impractical.
We had eight people there. I told my family not to come (flying in from out of the country with little notice was an expense that I didn't want to burden them with). My husband's mom and stepdad came, along with two siblings. Plus a best man/matron of honor and two other guests. His mom was the minister.
My husband had some anxiety about the guestlist - he's from a smallish town where culturally, everyone comes to your wedding. He knew that if he had his dad there, then his stepmom would find out and if his stepmom found out, then his grandma would know and then everyone grandma ever met or was distantly related to would be at our wedding.
In retrospect, he should have let his dad in on it and told him to trick grandma into getting into the car so she could be at our wedding. It has been a sticking point for years for the stepmom and grandma. They were pretty insulted. My husband wishes his dad could have been there (although he was not insulted).
People still pay attention to you. But there are fewer of them. People you don't invite will ask you about your wedding/motives. But it's not too bad.
- The awkwardness - being unsure who to invite, and potentially offending people that we don't
It doesn't go away. Actually, to make up for it, the stepmom decided to throw us a 10 year anniversary party. During which she recreated wedding scenes (since I "didn't have a wedding"): the best man speech (given by someone who was NOT the best man), cake cutting, riding off in a car, and insisted on referring to me as only "the bride."
During this party, grandma reminded us repeatedly that we had not invited her to the original wedding.
You can pretty much avoid this... unless someone throws you a weird fake wedding (above).
- The food - we're both vegan and would like a vegan wedding as whilst we have no problem with people eating meat/dairy, from our (limited) experience of weddings there's generally a lot of food waste
You could go pot-luck style or BBQ and just send home the leftovers with guests. But obviously, not having a big reception is the best way to avoid it. We went a restaurant after our wedding - with 10 people total, it wasn't a problem.
- The waste - we already have too much stuff. I feel like even if we implicitly ask for nothing, people will still (out of kindness) get us gifts
They will. But very few people will get you gifts if you elope. Some will still get you something (parents, for example). If you have a wedding, people will bring gifts. That's the way it goes. What's more, people get oddly offended when you ask them to donate to a charity or give you money. If you don't elope, just suck it up and register for stuff that you want or can donate.
Eloping wins hands down. I would choose to elope all over again. I never, ever want to organize a big wedding.
If you can, do it small-style, in a park or someone's yard. Invite immediate family (parents, siblings, grandparents) - if they are local. Your call on friends - none of our friends were offended about not being invited. Four unrelated people attended our wedding - two were formally invited (the best man/matron of honor) and two showed up when my husband gave a shout-out to his friends on 24 hours notice, essentially saying "If you want to come, then come, but it's not expected." The location of the ceremony was 4 hours away from our home, so that probably helped cull the herd.
If your families are small, then the 24-hour-shout out works well for friends - invite them for a drop-in reception at your house. If your families are large, then I advise you don't invite any friends. Then you tell people that it was immediate family only, because you wanted it to be small. Your goal should be to keep the guestlist to 20 people or fewer.
If not everyone in your family is local, then the courthouse is a clear winner for eloping. Real easy to use geography as an excuse for not having a wedding.