OK, so I got around to looking at the rear gearing. Nothing seemed disproportionately out of whack (there's so much "slop" in these older bikes anyways). I compared the new cassette to my old cassette and while there were differences between the 2 cassettes in how the spacing was done for the 6th and 7th gears (relative to each gear), it all seemed to match up just fine.
I checked to see if there was any slippage of the 7th gear on the freehub, and neither the gears nor the freehub showed any signs of metal stripping or fatigue (I thought there might be some odd spacing issue and the 7th gear wasn't seating down onto the freehub causing a problem). So, it seems the gears are remaining in place just fine.
There were 2 things I did notice, but I'm not sure how much impact they might have. First is that while the main cassette body (1st 5 gears are riveted together) sits (mostly) firmly onto the freehub, the 6th and 7th gears seem to have a bit more play when installed. Like I say above, tho, I saw no evidence the gears were slipping. The 2nd is that if I spin my rear wheel fairly fast (opposite direction of engaging the freehub cog), I notice a very slight "wobble" between the wheel/wheel hub and the cassette. It would seem that I may have a slightly bent axle. It appears that the more serious part of this slight wobble is down by the lower gears which means by the time the wobble gets to the upper gears, it doesn't seem to have much effect.
Good news is no serious problems found (other than I prob'ly should replace the axle). Bad news is I have no idea what's causing the slippage when I "stand on it" in 7th gear. It could very well be some off-the-wall compatibility issue between the chain and cassette. I reinstalled the cassette and hit the lock nut with a reasonable amount of torque (w/out over-tightening it, tho). I'm doing a short ride tomorrow, so I'll see if maybe I just happened to solve my problem.
I'm still open to hearing any ideas anyone might have about this.
Thanks and cheers....Steph