Dd was like this and she was breastfed - I think some babies are just prone to it, so I don't know if the brand of formula would make a change.
I used to keep dd upright for as long as possible after a feed - she took ages to bring up her wind. sOmetimes she would end up sleeping upright.
One of dd's issues is that she's tongue tied, so her tongue is "tied" tightly to the bottom of her mouth. It can be a big problem for breastfed babies, but I would imagine that babies using a bottle would need to be able to cover as much of the teat as possible and have a good "seal" on the teat so extra air doesn't get it - just a theory - might be worth getting your GP to check (my HV hadn't heard of it) It can stretch over time by itself or might need a snip (doesn't hurt) by a GP.
Sounds bizarre - but also, I really cannot burp and I wonder if she's inherited my digestive system!!
Lying her down every so often seemed to speed it up. So she would lie down, cry, be picked up, burp then be carried for a bit. Infacol made a big difference, but only when we used it for every feed. If we missed a dose it really made a difference.
Agree with the tummy rubbing - there are special tummy massage oils which are meant to help relieve colicky/windy pains. I think Aromakids make them - it might be soothing for both of you!
When you hold your ds, have a v gentle squeeze just at the bottom of his ribcage, if it's quite firm, then he's still windy, if it's "squashy" then you could risk putting him down for a while.
Dd also had crossed eyes when she was windy too!
I'll see if I can find the rub oil stuff for you.
hth all the best