I don’t think it’s unreasonable to serve sandwiches, esp as you will only have finished your main meal a couple of hours earlier.
Having planned a wedding, personally my concern would have been that just sandwiches would have looked like we were really trying to cut back on costs (although our wedding meal was much earlier in the day & we had evening only guests so I do think it’s different to your situation). But the thing is you are spending An absolute fortune!
If it is the Day you & your fiancé want & you can easily afford this then fair enough. I personally wouldn’t be happy providing guests burger, sausages & sandwiches & behing charged £16,000 (although I know that’s not what you were asking).
I’m not sure if you said when the wedding was but if you have time & have only paid a small deposit I would seriously consider going elsewhere. If people want to be at your wedding they won’t mind travelling a bit (you say most are travelling anyway). If you are able to cancel I would do the maths & see if it pays off to move the venue (you might lose £1,000 for example but a different venue could be half the cost so still works out cheaper).
And as for a free bar, I’ve not been to any wedding where it’s a free bar. I’ve not been to loads (about 6) but not one of them had a free bar. I didn’t really think that was a thing anymore, and one of your guests complaining it isn’t a free bar is pretty rude & It sounds as if they are charging as if your guests are going to empty the bar.
It is very hard to please everyone for food but you really just need to please yourselves. bbq is a good o provide some choice (if that’s what you want) & they can be lovely (one of the nicest food at a wedding we had was a bbq although was chicken, kebabs, halloumi, veg skewers, Burgers, sausage, steak). There are other ways though you can ofter some choice- but I’m not sure it would be any cheaper!
I hope you have a lovely day whatever you decide. If you sick with that venue I would most certainly knock the free bar on the head. If people take the jump it’s one less person to pay for x