Good point. I was concerned about both generators tied to the same neutral bar in the panel. ...
... my concerns with the combined GND/NEUTRAL bus bar connections. ....
You don't show, however, I suspect the N-G bond is in the panel, and you show the gens have the N-G bond removed. These transfer switches are designed such that one can have the utility powering the panel, and individual loads powered from the generators. All three sources can be on at the same time. Doesn't sound like a great idea, but I don't see anything inherently dangerous - other than:
... (and he knows he has to float the neutral if he plugs into this ....
My guess that will never happen. Against the code, but not too dangerous.
... The client doesn't want to get a full house generator because of the fuel supply issue (no natural gas and limited supply of LP), plus he already has one generator ...
The fuel supply shouldn't matter. Same fuel for one bigger gen as opposed to two smaller ones. The issue I see is with two switch panels, loads split between the two, and only one gen (which will happen), she won't be able to turn on the ones that are needed. Maybe set up the switch panels with one as the "Critical Loads" and the other as the "Nice to Have".
None of which you asked.
As for what I think you are asking:
Not inherently dangerous. I don't see any code issue.
(well except an inspector bursting into flames as he walks by)
the worm