If I already have a package on my system that was installed using choco install <package> -params "params", is there a command I can run to view those params? This is useful, for example, if I need to re-run the full install command later (since I don't normally remember the params I used to install it initially).
There isn't a choco command that can help with that currently, no. For security purposes, those parameters are persisted and encrypted. There is a non-official utility tool that you can use to do what you want though, you can find this here:
https://github.com/CollinChaffin/DecryptChocoArgs
Decrypt and display stored Chocolatey package argument files for reference/troubleshooting