OP,
This may not appeal to you whatsoever, but I just thought it might be a way round your dilemma (well, sort of).
Like you, I love Polly as a standalone name.
However, if your DH's adamant he doesn't want the Polly/ Olly rhyme within the family, might he compromise if her Birth Certificate 'official' name was something else, with (in his eyes only a) nickname Polly? Then you can call her that as often as you want, but he can use the other one if point blank refusing to budge you can't persuade him/ wear him down .
I know Polly is 'supposed' to be the NN for Mary, but there's no law Thou Shalt Only Stick To So-Called Rules, surely. Paola/ Paloma/ Pollyanna/ whatever else you prefer instead?
I guess you'd have mentioned if you already had a son/ sons? I'm assuming he worries about situations where you're referred to as a whole family? i.e. "Happy Christmas, love from Wineapotamus, Olly and Polly" (in which case, "love from Olly, Wineapotamus and Polly" sounds fine anyway. Even more so, if older brother/ brothers are sandwiched between, too, though I guess you'd have mentioned if you already had a son/ sons? ).
Feel free to ignore what is probably an overcomplicated load of old nonsense, which might lead to major irritation and resentment from both sides! And calm serenity in late pregnancy is better all round.
Though Polly is lovely, Vita Anwen Rose still gets my vote
Good luck for your DD's birth...