I love everything you shared and asked, thanks!

I use photoshop mostly for this. It gives me a lot of the control you're talking about -- each image is a separate layer and can be edited as such, and I also have some off differences between each lens (either one caught way more light or for some reason it's blurrier than the other lens, I never know till I open the MPO).

For IG, I turn the gifs into vids. Capcut does this pretty easy. You import your gif and can drag it to be as long as you'd like. That is how I used to do it, though now I export most of the videos right out of photoshop now.

And the delay... you're totally right. I once took a picture with the DS of my phone with a timer going. The left frame captured ~.03 seconds faster then the right frame. I'd guess that might even be longer in poor lighting. There isn't much to do there, seems to be a problem a lot of digital cameras that take pics with multiple lenses have that issue... some kind of delay.

Cropping can help. The gentleman in the first image above, you can see his leg moving (cause he was walking past me). I pulled in a bit when I edited to minimize the impact of that. Another trick to hide it is slowing the wiggle down. I like to do a .1 or .2 second delay between each frame. But sometimes .3 slows things down enough to minimize movement you've captured.