Thanks for the info on your experiences,
dbledan. We'll have an appointment with the dealer as soon as I call them; I'll let everyone know of the outcome.
In the mean time, I've purchased yet another new regulator with factory installed pol nut, and installed it on one of my older grilling bottles that I'd just had refilled.
With either the factory supplied bottle, regulator & pigtail, or my Sunseeker regulator, or the new regulator:
With the connection to the WH corrected, the WH runs w/o issue.
The furnace runs fine for a while, then the flame changes to a jittery mess that looks like the gas is actually burning in the chamber but away from the burner tube, but it's still putting out heat. I'm not sure that it is supposed to do that as I would expect to see the same flames from the orifices in the burner tube throughout the run. This is concerning to me.
After fixing the leaking connection in the WH, I heard the odd noise from the furnace one more time, but have been unable to reproduce the noise since then. My son ran some test cycles last night in preparation for the warranty visit, but hadn't yet reported his findings.
Next, the stovetop is still behaving the same as it always did - it'll run fine initially, but 5-10 minutes into the run, the flames start shrinking and changing to orange tips. The stovetop has an additional regulator within the unit, so it's possible that regulator is faulty.
Perhaps there are/were 3 distinct issues: WH connection, Furnace issues exacerbated by the loose fitting in the WH, and the consistent stovetop issues.
I've bubble checked all fittings and have found no other leaks, as well as checked the tightness at each fitting. There's nothing in the lines - they are all clear as the day they were installed.