I think Aldridge should be happy in SA. For some odd reason, though, he seems to view leaving Portland as a mistake. I'm just not as certain as you are that he won't want out, though I do agree he likely will play out both years.
I don't think the Spurs will let the Leonard trade stop them from letting Poeltl walk if the money doesn't make sense. Poe is a pretty prototypical modern big, so I see him getting way more interest than someone like Brook Lopez did. It's just more of a timing issue than anything. The Spurs let go of legit rotation players in both of the previous years they used cap space. Even if they don't sink it all on a big fish, they aren't likely to return all of Bertans, Beli, Forbes, Murray, DeRozan and Poeltl in that off-season.
Again, I don't think Gay views SA as a necessary partner. He "gave up money" to go to a contender, and the Spurs don't look to be that right now. Sure, he seems to like it in SA, and he has friends on the team. But both sides had to agree to a one-year deal, and I think that lack of commitment is telling.
I know your views on the modern NBA. Pop doesn't seem to share them. He's not playing Poeltl and LMA together to change things up. He's doing it because he believes in the potential of that unit. Even though it's not hard to find a third center, it's not easy to find centers that can make a lineup with LMA work. Like Kanter may well be a good backup center next year, but if Poeltl gets hurt, he's not going to be able to start next to Aldridge. Pop COULD go small in response, but I don't think he'd want to (even though it's up in the air if Murray's return would even allow for two bigs). Getting a third center who could play with Aldridge and maybe Poeltl would be Pop's dream, and such a player isn't nearly as easy to find as the scrapheap centers. I get that you don't believe that Goga, Bol or Porter can play that sort of role. But PATFO might think differently, especially after a year of development.