OK, I'm learning more every day...
I noticed for the first time the "Debug" option (next to the "Verbose" option) in Tools|Configure Lazarus Build... That's to say, I saw it before,
but for some reason I didn't think to turn it on!

So this appears to have "solved" my "problem". The warning dialog now respects the setting of the Warn flag, and I can now see some useful debugging info in my (fancy new date-and-timestamped) log files.
The debugger still shows <Error> for many variables (particularly non-core-library function calls and comments, but it does now return useful values for commented words, so things are looking up!
And I still can't run the project within the IDE if the project has an icon assigned, but that's a different kettle of fish.
I'm so sorry I didn't think to check that option before... I must have seen that option form at least forty times in the past week, and it just didn't click that by checking those options, I could enable and disable those two features. I just assumed that it was the '-vXXX' options in the project options form that was enabling all the verbose stuff.
Still, it's been really great learning about the way the debugger works, and some of the strange interactions that happen when unexpectedly stupid configurations are tried!
Thanks for pulling me in the right direction, and I'm so sorry I totally missed the IDE build debug setting.
Cheers,
Sheepish Pete