Happy ending
I've returned the Alivio, but I don't think it looked quite like yours. Is yours a 2019 Alivio SGS? I'll grant your theory could be true: I considered it at length before deciding to install inboard. On mine, going on the outboard side made no sense; it just wasn't made for that. So I'll say what I observed.
Although it was no doubt true in the past, it is no longer true that Shimano 9-speed road shifters work with 9-speed MTB derailleur. As my original post described, I tried to use my road shifters with an Alivio MTB derailleur, and found the shifters don't pull enough cable to move the derailleur from gear to gear.
Shimano CS rep. told me road and mountain 9- speed have different cable pull ratio, and he is correct. I ordered a Sora road derailleur and installed it, and it works properly. So folks should stop saying all 9- speed gear is compatible; I can attest that it isn’t, at least for the models in my O.P.
When I had the Alivio MTB derailleur on the bike, I had to shorten the shifter cable to try it, so going back to a road shifter required a new shifter cable. But I was fortunate to be able to return the Alivio for a refund, so I didn't get burned too badly overall. And most importantly the Sora works just fine with my 11/36 cassette, even though it's only spec'd for 34t max.
So the project was a belated success and I've got an 11/36 instead of 11/26 cassette. By the way, the spacing of cogs is identical on the MTB cassette that is now installed as it is on the road cassette I removed. I held them together and eyeballed it; they're perfectly aligned.