Where/how do I change the Payment Type options:
You need to do a little hacking to do adjustments to payment types. I haven’t tried it myself but editing the following should work just fine for you. 
File: modules/Finance/src/Forms/FinanceFormFactory.php
Function: createSelectPaymentMethod
Good luck!
Roman is right for v20, although the database uses an enum, and so that would need to be edited too : )
However, for v21 an option for this has been added as we just faced it at ICHK. You can see the change in the commit below:
https://github.com/GibbonEdu/core/commit/786c30690a3150b35a539de8861aa6ac1a3dd575
v21 will be released on January 20th, 2021
Cheers!
Ross
In that case I might just have to make do with v20 for now and not try hacking anything. Thanks for your help.