Yes OP. Your post sounds exactly typical for a parent of several small kids, let alone multiples.
I'd really encourage you and your wife to find one thing you each get to do that is personally restorative. Maybe it's swimming for you, maybe it's one night out a month with friends, maybe it's a class, etc... But carve out something that is just for you. Then carve out one night a month that is your date night (or equivalent). Throw money at that. Structure things so it's manageable for the other spouse. But prioritize that kind of time for each other and it will pay huge dividends.
It sounds like you have a good handle on the "throw money" solutions (which I TOTALLY support) so you're probably pretty close to working this out also.
It will get easier as your kids get older, but you'll probably also go through a tough patch when the twins are 2-4 years old and highly mobile, emotional, and irrational.

(That's where ours are now.) So get your protected time set up now and it will be easier to maintain.
Hang in there!