I spoke too soon. Just had to reboot modem and router again... grrr. It's faster than before, but still bogging down for no apparent reason.
ETA: another update. Apparently my rogue network message is something that dates to an Apple security update. It may be that those network changes caused by that are what have been making my connection cut in and out, hence need to reboot router all the time. Have done "fix" for that, and the rogue message has now gone and things seem to be working. Fingers crossed again.
ETA Again: curses. After all that, I still had to reboot the router again just now. Curses curses curses. I think I've exhausted all possibilities...
ETA: another update. Apparently my rogue network message is something that dates to an Apple security update. It may be that those network changes caused by that are what have been making my connection cut in and out, hence need to reboot router all the time. Have done "fix" for that, and the rogue message has now gone and things seem to be working. Fingers crossed again.
ETA Again: curses. After all that, I still had to reboot the router again just now. Curses curses curses. I think I've exhausted all possibilities...