So, it turns out we can leave for Iceland a day earlier than I originally thought, which gives us 7 full days (8 nights) there, not counting arrival day (~7 a.m.) or departure day (~5 pm), right at the beginning of October.
I notice there are both 6 and 7 day ring road tours available. I'm a bit hesitant to book a tour that would put me in close quarters with up to 17 other people for several hours a day, and I've read some negative reviews about the comfort of the minibuses. Indeed, if it's like the one we had on our tour of the Daintree Rain Forest in Australia, where we were stuck at the very back, shoulder to shoulder with a third person, that gives me pause. Getting in and out was a bit challenging for us--we're old and not that bendy--and we were stiff from being unable to shift position very much. It was fine for a day, though, but if we had to do that for multiple days, that would definitely not be ideal. When I do a test booking for one tour I'm considering (max 15 guests), if I book to start on Day 2 of our trip, there are 4 spots left, so the bus could be absolutely full. If I test book to start on Day 3, there are 15 spots left, which could be promising, but I'm worried it could also mean the tour gets cancelled.
Private tours are much too expensive in Iceland.
Another option could be to book day tours or 2-3 day tours to the Golden Circle, the South Coast, and the Snaefellsnes Peninsula. It would be easier to deal with any discomfort for a shorter amount of time. But I have FOMO and don't want to miss out on seeing some spectacular Iceland scenery on what will likely be our only trip.
We'd rather not drive. Although we're used to winter driving, I absolutely hate it, and the driver would miss out on some of the scenery. It would be stressful. Also, since this is somewhat last-minute, it might be a hassle to try to book our own accommodations and such. We would also have to rush to get International Driver's Licenses, try to book a vehicle, etc.
So, Ring Road or shorter trips, closer to Reykjavik? Would we be missing out on a lot if we do the latter? (I suspect so and am prepared to suck it up, if need be, to see more.)