Are there any weird quirks or challenges that come up when installing a short throw shift kit in any j-body car? I want to be doubly sure before I start digging into it.

Specifically I drive a 2001 2.2 5-Speed Manual Chevy Cavalier Base Coupe.

I'm a 2nd gen, but you may be able to mod your shifter to get a shorter throw. There is a thread on "How To" at https://www.v6z24.com/threads/how-to-make-a-short-throw-shifter.142498/#post-1562598
The example is a gen II, phase II, but it will give you an idea of what 'might' be possible to do to yours.
Some of the 3rd gen guys can tell you how best to get what you are looking for. Hopefully they'll offer their advice.
Good luck