So, I did some digging into this today and called the town clerk who issued our marriage certificate, along with NY Vital Statistics. It looks like there is no option to amend the marriage certificate to remove the middle name change. I was told that I could go through the NY State courts to do a name change, but I feel like that is another can of worms entirely, I don't even live there yet 😅
As it stands now, I could:
Assume my husband's last name here in British Columbia, but my ID won't match the marriage certificate without further legal adjustments to my name somewhere down the line.
Do the legal name change (which currently has a processing wait time of 24 weeks, and our vital statistics and postal services are on strike right now). All my documentation would match, and my birth certificate would change, but I'd be issued a certificate of name change which lists my prior name along with the new name. I believe I can also obtain a certified copy of my birth registration, which while not used as an identifying document, would still list my name at birth, matching the certificate of name change. Based on the current I-130 processing times, this could still be completed well before I reach the NVC stage.
I also looked more into the name change during naturalization in the US, which I know is also a legal change of name, but it was difficult for me to find straightforward answers on if that would necessitate me changing my Canadian birth certificate after doing so. And I would still be updating all my ID, etc. across the board to match the name change after that was completed.
One thing I am still uncertain about is how much the listed name on the marriage certificate matters, or if it's going to cause problems down the line for me if documentation doesn't match the marriage certificate in either Canada or the US. Especially with NY Vital Statistics telling me I'd need a court name change to fix that.
It seems I still have some thinking to do on the matter. Thank you to everyone who has commented or shared their experiences with me so far, it's truly appreciated!