Really the "right" way to go about it would be to employ an existing package manager (there's enough already, we don't need another) and some magic glue on top that makes it easy.
For example, you have your configuration of packages, in the ephemeral cloud somewhere, and you do the really dangerous no good thing of piping through bash with some kind of uuid that's assigned to your account, something like (totally made up url)
curl packman.info/users/aed1242faed60a | bash
And it sniffs the architecture, version of binaries to install, which ones are there, and then puts it into an install directory configured by you.
This is like 97% existing things with a little glue and interface polish so you can easily bring in an environment.
There's certainly other ways but the idea remains the same
For example, you have your configuration of packages, in the ephemeral cloud somewhere, and you do the really dangerous no good thing of piping through bash with some kind of uuid that's assigned to your account, something like (totally made up url)
And it sniffs the architecture, version of binaries to install, which ones are there, and then puts it into an install directory configured by you.This is like 97% existing things with a little glue and interface polish so you can easily bring in an environment.
There's certainly other ways but the idea remains the same