These old Sun rims have a pretty deep well
Is the well what I would call the spoke channel?
Usually if you are having difficulty putting on a tire, then it's because you aren't keeping the bead of the side you are currently attempting to put on in the spoke channel. The side that is already on completely has no business being in the spoke channel so push it out of the spoke channel as you push the other into the spoke channel.
Tubes that mysteriously blow out after the first ride or maybe a dozen rides after installing is usually because they were damaged during the installation of the tire. Always do some investigation to find out what caused a flat. It's easy with good habits.