Custom Install Directory
I believe a custom install directory would be useful. I have a lot of my dev stuff on my USB so I can bring it around. Being able to install Roblox studio to my USB and do all of the normal stuff from the USB without needing to make directory junctions or anything would be great since I can just plugin the USB and launch studio immediately.
So I finally gave myself a chance to look into this issue today. While it's possible to add this feature and I've done so in my current branch, I'll need to do some additional work to automatically make it as portable as you're describing.
The program stores the state of the mod manager in a registry key which isn't directly portable, so you'd need to import and export that manually. If I start serializing this data in JSON within the studio directory then that should suffice.
I've started work on it here using a registry solution. If you'd like to opt-in early you can take a look here: https://github.com/CloneTrooper1019/Roblox-Studio-Mod-Manager/tree/custom-install-dir
Note that this won't be forward compatible with whatever JSON solution I come up with, I just don't want to spend too much time working on this right now since I need to focus on my job.