I will not ague the engine out procedures, ( the TA in there ,as I learned recently,was mostly to prevent " coordinated" climb RAs ) , but would like to go back to the original question : during an emergency descent :
From an ATC point of view :
After having witnessed many such events trained in the sim , with different airlines, and relating this to my own geographical area , I would advise a turn of 15 min max 30 degr ( to get you out of the traffic on the same track below ) squawking as soon as possible A7700 ( to warn all other ATC ( civil and/or military ) units below of what you are doing ) and finally keep the RA on, as, if this is happening near an point of convergence , ( FFM, SPI, or TRA to take some European examples ) you are most likely going to meet a lot of people on your way down. I believe also that with the rate you are going to descent , you are more likely going to get RAs like " monitor vertical speed" , of "Adjust vertical speed ", and the others will coordinate their RAs accordingly.
As someone else said earlier , better breathe O2 a few seconds more and keep on breathing in the end. .