... including, I presume, KDE Connect?

I feel your pain, I tried tons of other solutions before discovering KDE Connect. It works well for my laptop/phone combination, but I'm not surprised if it doesn't work for others, given how horrible each other solution was that I've tried.

edit: I wonder if perhaps some part of your phone hardware overheats after N megabytes because it's not built for constant file transfer, or constant file transfer using these protocols at least? What if you try throttling it on purpose?