'I think the other aircraft involved will get their RAs modified in the light of you not following yours.'
I'd like a definitive 100% black & white answer to this question. So far in trying I've been unsuccessful. I think the time bubble that envelops/protects the attacked a/c would not give TCAS RA the time to change its mind and issue commands to the 'innocent' a/c to run away and give the crew time to react.
The 'note' in the Engine Failure QRH when selecting TA Only mentions only that it is .........to avoid climb commands.......There are far more scenarios where this should be selected. In this case I'm amazed that it is No. 9 in the sequence. IMHO if your performance is compromised TA only should be ASAP.
And; in a Volcanic Ash scenario where both pitots are effected by ash + engine flame out and you are in 'windmill start' envelope so you need speed (even worse in a total flame out where speed is vital & thrust is zero) and now you have an 'unreliable speed' event; I expect the ensuing confusion as to which memory items to follow accompanied by a massive CRM breakdown would be entertaining. The 'old grey beards' might come into their own.