Apple Support was, indeed, the key! Suspect my problem isn't all that common, but in case someone else has it, it may be worth sharing what I learned and what happened. I had an excellent talk with Micah of Apple Support, who laid out three different ways we might go about transferring data to the new laptop and — to my surprise and pleasure — offered to stay on the phone with me for awhile as we initiated the recommended approach, to be reasonably sure it was working before we parted company.
To my surprise, the recommended Plan 1 was to connect the two computers using WiFi with both computers in normal mode, even though my experience had been that the old one pretty much lost its Internet connection only 5 minutes or so after being booted in normal mode. Micah's point was that Migration Assistant shuts down other software and there was reason to believe (at least hope) that might avoid my problem, since we knew it went away in Safe Mode when some software is disabled. A fallback Plan 3 — thought to be OK, but a bit uncertain for us both — if Plan 1 failed for loss of connection, would have been to boot the old laptop in Safe Mode.
Plan 2 was to purchase a new Thunderbolt 2 cable and a Thunderbolt 2 to Thunderbolt 3 adapter and connect the two computers by cable. In retrospect, this probably would have made the transfer quicker than it turned out to be, but would have required spending ~$100 for a one-time use cable and waiting several days for it to arrive.
As it turned out, Plan 1 — WiFi, normal mode — worked, though very slowly. The two machines never lost connection, but steadily transferred data at rates only ranging from 17-36 Mbps. (At the same time, my iPhone measured the WiFi connection as capable of handling over 400 Mbps. The new laptop actually had a message saying things might go faster by cable.) So, starting late one afternoon, it required waiting overnight for the process to complete — but complete it did. And Migration Assistant made the getting connected process easier than I had expected — e.g., I didn't have to tell it where to find a WiFi connection, it immediately showed me the available options and all I had to do was provide a login password for that.
Before claiming the entire process of migrating to the new laptop is complete, I've still got a couple of applications to wrestle with — licensed on the old machine, but their licenses are not recognized on the new one — and my Time Capsule for some reason refuses to connect to the new laptop. Frustrating issues, to be sure, but they are different and separate from my big data transfer issue and question raised here. Migration Assistant and a pleasant, helpful, and caring Apple Support representative got that problem resolved. Thank you to both!
