Just the man I was hoping to hear from! Thanks for clarifying that and for the link.
I found some tape at a local RV repair and supply company. It is grey and about 3/4" to 7/8" wide and 1/8" thick. I don't remember the width exactly since it is now on the boat, but I do remember that it was about 1/4" to 3/8" wider than the flange on the window; I had to cut that much off before fitting it in place. Cutting off the excess was a challenge; you need a sharp razor blade or box cutter type knife and keep the blade clean or the tape will tear instead of cutting cleanly.
This stuff is very sticky so you have to be careful when putting the window in place. Once it touches the cabin surface that's pretty much where it's going to stay. It's not something that you can kind of "wiggle" into place. If it's not in the right place you'll have to pull it all off and start over with a new length of tape, otherwise the tape will stretch and you won't have the thickness you need. (I guess you could re-work the material and apply it around the flange again, but I was trying to get a continuous, flat, even thickness of tape all the way around the flange.)
My first attempt didn't work because I had to angle the front in first then push the back in. The butyl grabbed on the front and I couldn't slide the window back to even it up in the opening. I had to shave the opening a little to allow the window to drop straight in.
I wish the width of the tape were narrower but I like the 1/8" thickness. 1/16" seems like it might be a little thin for those frames. The inside of the flange is a little bit concave around the bends, so the tape needs more thickness to fill that area.
I've done some pretty serious water hose testing and so far there are no leaks.