Congrats on the twins! I also had two older children when my children were born and did cloth full-time right from the beginning with them. Not in the hospital but that was pretty much only because I was afraid a well-meaning nurse would throw them out or something (I had a c-section unfortunetly so they spent some time in the nursery).
Anyway, there was no other option but cloth for us. And I can't even claim that it was really for environmental or even financial reasons. Of course those were fabulous and important to me, but I would have done cloth even if it was more expensive and not as good for the environment. I really do think it's easier overall, even with the additional laundre. With 4 kids laundry is a constant so 2-3 extra loads a week is barely noticeable!
As for nighttime, our experience has actually been the opposite of yours. For my twins disposables didn't leak that much at night but with my first two disposables were horrible for leaks and blowouts!! With my first if I used a disposable at night she'd be guaranteed to wake up wet and if I used them during the day during her first 11 months (she wasn't fond of solids so had those explosive breastfed poops for a long time!) I'd be guaranteed to get blow-outs!!
Anyway, for the nighttime thing I say just don't even worry about in the beginning. Just do whatever works for you until you feel you have the courage to try it (if you do). While I'm a big fan of cloth at night, the fact is that having two babies at once can be overwhelming in the best of times and you don't need any additional stress. If you feel like trying it then know that we'll be here to help you out IF you need it (considering my experience and that of most people I know, chances are that you won't). Just off the top of my head I'd say that if you were using the pockets that could well have been the cause, pockets are way more prone to leaks from repelling and if your little one pees fast then it doesn't matter how much absorbancy is under that fleece, it'll just run off and out the diaper because the fleece won't let it through quick enough (even if they're fine during the day). Overstuffing a pocket can actually make things worse as there needs to be some movement and 'gaps' between the fleece and inserts or else it'll make repelling that much more likely. Just some random thoughts off the top of my head....
And if you don't ever want to try, then in reality it's just two diapers a day... Still a huge savings of money and the planet over full-time disposables!
If you do though, maybe minimize the mess potential with a couple of these tips... First, if the weather is hot enough, maybe try just a diaper alone with no pj bottoms. I don't know what the weather is like where you live or when your little ones are due but here in the summertime my kids would often sleep with just a t-shirt or even sometimes with nothing other than a diaper! If you can do that it'll at least be one less layer to change should a leak happen.
You could also maybe try layering the sheets on the crib (if baby sleeps in a crib). You put one fitted sheet, then a waterproof layer of some sort and then another fitted crib sheet. If a mess happens (this could be useful even for just spitting up for example) then you just take off the first two layers and you're good to go! If baby sleeps with you, have their bum on a waterproof pad of some sort, or maybe even a towel. If it gets wet then just chuck it in the wash!
I don't think these things are really necessary but maybe using them will give you enough reassurance to eventually try cloth at night again...
Oh, and don't invest in too many additional diapers. I went a little crazy with mine and forgot that although I had two babies, I still only had one washer. It doesn't matter how many diapers you have, you're limited by how many will fit in your washer at once. More will make your life easier to a certain extent but you don't need double what you'd need with a singleton.