Have you tried looking inside the door controller itself rather than at the remote?
From memory mine has a number of inputs including separate open and close, alongside the multi-function one that goes with the standard remote. It also has a “door closed” output that is a simple contact that doesn’t require lasers or ultrasonics or any of the other more complicated suggestions!
Even if there isn’t a permanent input, some controllers have assignable inputs so you might find that one can be assigned as “close”.
Would be a lot easier than sensors or measuring devices.