Should I abandon the ATS idea altogether and focus on an inverter-charger with that "built in"? I don't need a lot of capacity here.
My experience with in-rack ATS is that they cause more problems than they prevent. There is a fundamental design issue that different manufacturers have tried to address with varying degrees of lack of success.
The ideal transfer switch has both inputs in-phase and a near-instantaneous transfer time. However, you can't guarantee that both inputs are in-phase. Even with 120/240 power you have a 50% chance of being 180 degrees out of phase, and your odds with 3-phase are even worse. If one of the inputs is the output of a UPS, there's no hope of being in phase while on battery. I haven't found any manufacturers of rack ATS that use SCRs on both inputs (relays on both is most common, while SCRs on only one input can be found at a much higher cost). So you have a variable mechanical delay as the relays switch from one input to another. You can end up in a brief state where both inputs are trying to drive the ATS output. If you're lucky, one will "win" and still power your load. But it is much more probable that you'll be unlucky and you'll trip both of the feeder breakers and/or weld the relay contacts in some position.
Even if your equipment is in a datacenter and they 'guarantee' everything is on the same phase, that isn't always the case - I've had to show datacenter management that the 2 "Phase C" circuits we had were providing 208V between the relevant "hot" legs instead of the expected 0V if they were on the same phase. And even if they really are on the same phase leg, your ATS can try powering everything else on that panelboard via the other ATS feeder, leading to a breaker trip (either on the ATS or the panelboard supplying it).
I think you would be much better off with a UPS that provided internal bypass or had an external manual bypass switch. The external switch is good because you can test the whole UPS out-of-circuit when needed. APC actually built a manual bypass switch for the Symmetra RM, though it was semi-custom for a large telco and didn't appear on the price list.
Speaking of datacenter and phase follies, one place I worked had a TV studios in 2 different buildings a few blocks apart, with underground conduits full of coax cables and control lines running between them.. They had equipment that kept blowing up inputs, etc. Some genius determined that there was a neutral voltage imbalance between the two studios and decided to run a piece of 4/0 copper between the two buildings to "equalize the grounds" on the theory that the neutrals would follow, since neutral is bonded to ground at each building entrance and by definition everything on the electrical grid is in phase. They put a lug on one end of the cable and bolted it to an I-beam in the R building. When they tried to do the same in the P building, brushing the lug against the bare metal of the I-beam resulted in a "Thwomp!" sound that was apparently audible in both buildings, followed by the 4/0 cable tuning into a flashbulb and vaporizing somewhere in the conduit system. The conduit and contents were a complete write-off and had to be replaced. When they spoke to the power company, they found out that while the two buildings were only a few blocks apart, they were fed from different substations. Made a heck of a "ground loop" while it lasted. Moral of the story - sometimes being in phase isn't enough.
