Using the two APW3++'s you have as your described will be just fine - so long as they are, as you indicated, on separate circuits.
Rigging a power cord for your electric dryer outlet, if not in use, might be easier - since its unlikely your going to find 2 separate circuit 110V outlets close to each other. You would just need a male 30amp dryer plug on one end, 12 gauge (yellow coated) wire for the run, and whatever plug you need for your APW3++ on the other end. Then you could use a single APW3++ to run it.
Note a step-up transformer is not magic - its going to pull all twice the 220V amperage on the 110V input side, plus waste a bit of power doing it. e.g. Blown breaker.
I do have a dryer outlet like the one I've linked to below that isn't in use since my dryer only requires 110v and is plugged into a normal outlet. That was by first thought, but I cannot find the right combination of cords or adaptors that can make it work. When I was googling around for an answer I found one guy who said it's impossible for some reason, but who knows if that is correct. I don't want to jerry rig something though by splicing wires myself, be it from this outlet or from my breaker. Saving a little money isn't worth burning my house down or zapping myself.
https://images-na.ssl-images-amazon.com/images/I/71ngHbefakL._SL1500_.jpgTo be 100% clear though, having a single S9 in the house is torturous (as long it is not in the basement).
The sound that this machine makes is simply incredible and not in a good way.
It's gonna be in the basement. I already have an L3+ down there as well as a furnace that is cranking away all winter making noise.