It's looking better now. Half dozen Sony +R, all readable, no more mechanical distress. It is necessary to finalize each DVD manually, even though it auto-finalizes at the end of each disk. There must be 2 somewhat different processes the machine calls out as 'finalizing'.

That's good news -- I'm glad to hear it's working well now.

Based off what you've said, it seems to have two processes:
1. Finalizing the recording, so that the disc menu works correctly.
2. Finalizing the disc, so the DVD can be played in players and other-brand recorders.

I would not worry about that, it's normal. It's just not usually called "finalizing" for that first one, at the end of a recording. Let's be honest, it's probably a bad Engrish translation. These things are made cheaply in Asia, after all. Some of the manuals found with DVD recorders make for comedy reading, it's just horrible English, often with wrong words. I'd bet more than anything that this is the issue here.