I replaced the skylight over the shower on my last trailer (2018 salem cruise lite) after a storm tossed my shade tent onto the roof. My dealer wanted over $250 to replace this skylight.
This is the product I purchased, its a better quality dome than what the factory installs, much thicker and less flimsy. Of course 2 years ago it was about $20 cheaper than it is today. I chose the white version so it would not yellow over the years in the sun. The white version lets in the same amount of light, it's just not as intense as the clear version.
ICON RV Skylight - SL1422W - White
https://a.co/d/eH9PGo3
You will need a flexible putty knife (I used a metal one because it's thinner than plastic and rounded the corners with a sander) a roll of 1" butyl tape, 2 tubes of dicor self leveling sealant, and denatured alcohol.
It will take you the better part of an hour or more to remove all the old dicor around the old skylight. Take your time so you don't tear a hole in the roof membrane. If I remember correctly I had the same size cutout as you have. This dome will fit just fine since it's slightly larger on one dimension than the actual ceiling cutout.
I reused the screws from the factory skylight because they are square drive. I had to use a pic tool the remove the dicor from the square holes.
DON'T over tighten the screws during reassembly as it can crack the new skylight.
Some Pics of my repair
Removing what's left after the dome is out is the labor intensive part
If I was to do this again I would have used twice the amount of dicor. It never leaked during the time I owned it after the replacement
Here is the video I watched before attempting the replacement. This guy is wrong about using Dicor on a PVC roof. Dicor is labeled for PVC roof membranes.
https://youtu.be/qkRhyn2Q70s