Thank you for the idea. I did not think about a "wet" dry run
It seems to me that you can't have it smashed up to tight or you will squeeze out all glue. Having said that, you do want solid wood on wood contact...
Interestingly enough, when I'm watching the videos of repairs most people seem to do a visual inspection of the dry run.
It makes sense to me that the glue/ swelling of the "wet bridge" will take up the last bit of paper thin space.
I am still going to do more investigation though and I will try to heed all advice before proceeding with the wet run. With Titebond, worst case I end up repeating process and or giving up and heading to luthier.