We just sailed on the Magic - 8/21 Eastern Caribbean and had the same situation. I booked last July before I knew my wife was "with child" and choose late seating.
I originally put ourselves on a wait list for early seating, but after discussing it further with my wife we decided to keep late seating.
In case you are not familiar, if you have late seating (8:30) then you go to the early show (6:00). The choice was to have Sarah eat with us early and fall asleep at the show or vice versa.
Booking Flounders every night just didn't seem feasible so we kept our late seating, Sarah enjoyed the shows and then usually fell asleep during dinner.
Most folks park their strollers at the entrance of the restaurants, but depending on table location you might find the room to park it out of the way by your table. More times than not we left the stroller outside and just brought her in the car seating.
During lunch and sometimes breakfast the restaurants aren't that busy so it is easier to find a place out of the servers way, although in true Disney fashion they always try to accommodate whenever possible if you really want to bring it in.
For the record we did book two more cruises and chose early seating for both. My wife also gets sleepy by 10:00.
Jeff