Maybe I'm in danger of starting to feel I know what I'm doing... but 'Squawk XXXX and pass your message' has never bothered me. I do exactly that i.e. dial in the squawk (short pause therefore while I do so, though modern transponders do make that easier) then pass the message which, after all, I was expecting to do so I have already thought through.
I do think the 'pass your message' spiel gets a lot easier with time. It used to worry me a lot. So the message to the OP is keep at it, like everything else in flying it gets easier with time.*
*apart from landing which seems to go in waves.