Once again, a big thanks for all of the informative feedback. You've given me plenty to think about.
For those of you who are curious about the suggestions given, here's a count / cartridge synopsis in count order & caliber order:
View attachment 735473
The top two choices by a large margin are still in the lead & almost tied: The 25-06 & the 257 Wby.
Rebarelling my LH Remington 700 to a 25-06 or a +P 257 Roberts would be a cheap & easy option that wouldn't add another rifle to my safe. It would leave me room for that cast-on SxS shotgun I've been pining for.
The 257 Wby is also an easy option since it only involves pulling a credit card out of my pocket & picking one of the left-handed rifles that is readily available. My only current choice is plastic stocks with really long barrels so I'll have to ponder if that's what I really want (because usually I don't).
I have an outsized fondness for the 6.5x55 and I love my LH Sako in 30-06. Getting a LH Sako in 6.5x55 and setting it up to shoot lighter bullets would not make me unhappy at all. I doubt I'll be frugal but I do have this option in the Tikka T3x Hunter as well.
Attractive LH 270 Win rifles will pop up occasionally. It's nice to know other hunters are getting good results shooting lighter bullets with this chambering. About once or twice a year I will stumble across a LH Ruger MkII in 25-06 with a 24" barrel so it'll be interesting what the price of the next one I see will be.
None of these obvious choices negate the fact that I may do something totally different but at least for now, I feel like I'll be making a more informed decision. With left-handed rifle shopping, there's a lot of waiting, searching & disappointment. But when I see one that fills a niche, I sometimes have to act fast. So it's always nice to get the research & decision-making done ahead of time so I don't do something dumb on impulse.