Well, following up on this after having the TH-9800 installed for a couple months:
I've found I can in fact use the TV tower housed repeater, 60+ km from home, from my yard. I get spot dropouts for the first couple kilometers as I'm getting out of the draw I live in, but they're not a major problem. I can also use the "local" repeaters, on the mountain ~4 km from home, all the way to work (60+ km), except for local dropouts in low elevations near work.
These are 2m stations.
I also found a few weeks ago that I can reach a 440-band repeater from hilltops near home, at a distance of 60+ km, despite the repeater in question being roughly 15 meters above local terrain. I still can't reach the one with the mountain in the way (surprise, surprise...).
The 6m repeater I mentioned in the OP still works, from work to home, with some terrain dropouts near home (above 40 km distance -- and the repeater's owner reports it's getting tired and its transmit power is off a good bit form the nominal 50W).
Still haven't made a contact on 10m, but I haven't tried much -- I joined a weekday rag chew net that I can catch on my commute home from work, and don't have much reason to spin the dial a lot at present.
Looking forward to taking this radio and antenna on my next vacation trip, from central NC out to the Outer Banks; there are a number of 6m and 10m repeaters listed along my way, as well as the usual quantity of 2m and 70cm in every town of any size. With the flatter ground out that way, I might well be able to reach a 10m repeater in Rocky Mount all the way from Raleigh to the shore, if the repeater's antenna is high enough.