not announcing is not that big of a deal, i do it all the time. if they tell you not to announce, just ask for some information upfront before you connect the call. such as thier name, the reason they are calling. if they get upset over the questions, just explain this will help their call go smoother and have a better chance at suceeding at their intended goal of not knowing its a relay call.
use alot of fillers, so the hearing people know you are still there, cause hearing people fear dead air like the plague. you can also use "hold on" to the hearing people if you have a part that you need to clearify with the vp user.
as for the problems with "customer service" eh, i expierence all those things you mention, but as soon as the call is disconnected, those people are out of my life forever, if you let it get to you then youre making things worse for yourself. granted we get the same callers sometimes, even in the same night, if they complain about you, offer to transfer them to another terp, if they agree, lucky you. if not, grin and bear it.
ive had callers tell me i was too fat, tell me i need to learn sign, tell me this or that....on the flip side ive had calls go really well and applaud me and not want me to transfer them when i get off work. some people you jive with, some you don't.