YANBU for feeling a bit sad about not being able to have a bigger celebration; it doesn't sound as though you want anything OTT.
But well done for focussing on what is really important.
I think you have a couple of choices here
a) Really go with the quiet elopement style wedding. I've known a couple do this and they made it a really lovely romantic special day just for them. If you want to go home straight from the ceremony and celebrate in bed with a bottle of bubbly, a punnet of strawberries and a pot of chocolate sauce, go for it. Do you have a friend who's good at photography who can meet you afterwards at a local park/beach/garden/local tourist thing and take some photos of your first hour as a married couple. Do something to make it a bit special for yourselves.
b) Invite more people and do a low key cheap party with them. don't think 'reception', think party. As long as you make what is happening clear to them, they can decide if they want to travel etc. And to be honest, when you go to a wedding, you should be going because you want to be part of someone's marriage and celebrate that, not because you fancy a big party. All these massive weddings are lovely but really quite a new invention; even 20 or so years ago most people weren't doing all this stuff as a given. So...
find a pub with free private room hire, lots do this, people can buy their own food/drinks. The pub may even do a small buffet/snacks for you FOC if you bring enough people round to buy drinks on a day they are usually very quiet (midweek?).
Have a party at home, cheap buffet, BBQ or potluck with people bringing food. Make it a BYOB (most parties are, after all...)
Have a park party with people bringing their own picnics (make sure there's somewhere you can run inside if it rains, park cafe etc.)
When I got married my 'wedding breakfast' was a powl of punch and some snacks at my mum and dad's house for family. In the evening we threw a party at home for friends, same as any normal party.
I've been to a bring-a-picnic party - held at one of the couple's place of work with her employers permission. Do either of you work in an office with a nice big meeting room? Or a warehouse? (the one I went to was on a farm, there'd been cows in the shed a couple of days before and her family helped her scrub it all out and decorate and we all took food). It was a glorious wedding, remember every detail years later and way more interesting than one of those cookie-cutter hotel packages.