I'm not sure I agree with some of your points there, Ghost.
The TCAS fitted to our aircraft (757/767) is not fully 'performance aware', i.e the TCAS assumes full a/c performance (at current weight ?) available at all times and is not fed any data on engine failures or shutdowns.
It is therefore perfectly possible for an aircraft on one engine to be issued a Climb RA which cannot be actioned. Thus, as you rightly point out, TCAS boxes should be selected to TA in the event of an engine failure. I also don't see why, in your scenario, the climbing/level aircraft would, de facto, be issued a Climb RA. As I'm sure you are aware, there are a complex series of interactions between two RA-enabled TCAS boxes, and the results, though always safe, are not necessarily predictable, are they ?
An RA issued simultaneously to a descending engine-out 757/A321 and a climbing ATR would, as far as I understand it, be more likely to ask the jet to climb or monitor vertical speed, as the boxes would have agreed the jet has better performance available.
With your box selected to TA, the ATR would get a more appropriate RA as the ATR system would be aware that no resolution would be issued to the jet.
Very interesting topic this, and this is only my understanding of how the kit works. Wonder if anyone knows any better !