Snuggly I used to hang out with a bloke who was primary carer to a baby and toddler (his daughters) and had an autistic son. He had time saving pretty seriously sorted, and the way he coped was to buy formula milk in little cartons and to have lots and lots of bottles.
He would fill a lot of bottles in the morning and put one in every pocket of his combat trousers and his very expansive jacket, inside and out. Whenever a child cried he just reached into one of the many pockets and pulled out a pre-made bottle which was instantly ready to go.
In emergencies he just ran into boots and bought a new bottle and a new carton of pre-made formula, poured the one into the other and then stuck the bottle in the baby's mouth. On a really bad day, he also poured in a random splosh of calpol for good measure, without noting the time or amount.
It wasn't probably very cheap, or entirely ideal, but it did seem to get him through.
I knew another Dad who at the age of 52 had taken full responsibility for all baby night feeds from newborn to sleeping through, while also holding down a professorship and head of department role in his department. He also did the trick with the bottles and pre-made cartons of formula. I think it's quite pricey, but in a time-saving emergency it really seems to help.
Good luck there. It sounds like quite a job. Do they have a twins doula near you? There is one here, who can be found through the LLL and I've heard that she is very good.