Yeah. You could do either one. That's the beauty of maintaining the same rolling stock of LRT cars. You could run the red line under 8th and the SE-LRT on 7th ave. Or vice-a-versa. Mix and match.
The only problem is that the 8th ave subway is going to be ridiculously expensive. That's why I think stage one of the 8th ave subway/SE-LRT would only have stations at City Hall and Centre street. It would be a stub-line. Having a station at Centre street is still central enough for most people to walk to.
Is it though? It can be about 2km of shallow cut and cover, and the disruption cost is also minimal (compared to say 11 Ave).
I don't think you'd do a station at Centre St...but I think there is an interesting question here: if you were designing the 8th Ave subway with absolutely zero consideration to the Green Line ever existing (or say the assumption was GL would be on 7th Ave instead of 2nd St), where would you put the stations? I'm thinking the answer probably isn't 4-5 stations within 1.6km, as is currently the case for each direction on 7th, but rather:
1. City Hall, 5th Street, 5th Ave* (~1km apart)
or
2. City Hall, 2nd Street, 7th Street, 5th Ave* (~700m apart) *or maybe no station running N-S, though it would be nice to touch the NW corner of DT
Probably #2 for a bunch of reasons; #1 is mostly about overall speed.
But I think there is another interesting question to ask: should all of the 8th Ave stations be underground? I'm not convinced that underground is the better option operationally, without even considering costs. It can be a bit worse from a mobility standpoint. Protection from elements is nice, but can also attract an undesirable element...
I think you could limit it to a single cross-street interaction with a minor road (7th St, 2nd or 1st St). And you keep the tracks 35" below street level, so you're not actually building new platforms. Downside is you'd never really be able to expand to 5 car trains, but I think the better answer will always be frequency.
It probably only makes sense around ~7th street, but I'd imagine there are some benefits like managing HVAC for slightly shorter tunnel sections than one massive system
Olympic Plaza should certainly be underground...it is kind of a shame they're tearing up Olympic Plaza soon seemingly without any consideration of the future station.