First, great playing all around! The bass player doing the George Benson thing is amazing.
The tape idea works great, you can add the date you install too, which helps since they usually last me at least a few months.
You've almost definitely got a short for it to be failing so quickly, either at the wires or with the switch- watch that led on the back for sure.
One thing that might help in the short term- the screw slot is designed to work with a US dime, no screwdriver required.
You can get a better battery snap from digikey.com with longer wires for not much $$.
https://www.digikey.com/products/en?mpart=BS12I-MC&vendor=61As for modding the compartment for spring style contacts, it's a little tricky. You need a way to increase the depth of the cavity, and probably also open up the sides too. Then, you need to add foam which is strong enough to compress the spring contacts but not so strong that you can't get the cover back on. And probably most important, you need to be sure that the polarity is right. A 9V battery can fry stuff on the pcb if you hook it up backwards.
An easier thing to try might be to add the refined style battery box to your rear cover plate. This is semi-reversible too, since you can get a new back plate. The trick here is locating the box so it doesn't interfere with anything inside the cavity.
Good luck!