Should probably do some more reading on the HOM2200bb and HOM2150bb. The spec sheet simply says they are for load centers and combo units rated 150a or more. No reason it shouldn't be allowed, those breakers use 4 stabs which keeps the current at or below 100a per stab. Might be worth a phone call to Square D.
150a breaker with 2/0 aluminum wouldn't be bad to install as long as you don't predict your load going over 135A.
Otherwise the 200a with 4/0 will give you 180a of allowable load. I wouldn't mess with 250mcm, your whole house isn't fed with wire that big.
With that phase converter 100 feeder isn't enough. Full load on it is like 110A.
So after doing a little more digging, it seems like I should NOT use a breaker greater than 100A on the particular CSED I have. There's different versions of the 200A CSED, and I unluckily have the first version. I found a reply from a Schneider Electric tech from their website that states:
"These larger branch breakers can ONLY be used in the CSED that show them listed on the wiring diagram of the device.
NOTE: NOT ALL CSED WILL ALLOW THE USE OF THE LARGER BRANCH BREAKERS. The specific devices will be marked for a branch breaker of 200amps Max. So these high amp branch breakers, catalog numbers HOM2150BB, HOM2175BB and HOM2200BB can be used in those specific CSED ONLY, that are rated 150amp or higher."
I also contacted a Schneider Tech, and they confirmed that I cannot use breaker HOM2150BB on the CSED SC2040M200C stating that '"the panel was only engineered for 100A max. Probably due to heat dissipation and/or wire size". But I see what you are saying, that a 2 tab 100A breaker is okay, so why shouldn't a 4 tab 150A Breaker be allowed. Logically it would be like having a 2 tab 100A and 2 tab 50A breaker, or some similar combination.