I have no doubt DC is corrupt in many ways. Sorry for your experiences, and thanks for explaining the war among jurisdictions in the DMV area.
Regarding the handicapped stuff, all jurisdictions (except NYC) are required to honor "foreign" disability placards, meaning from other jurisdictions, mostly out-of-state. Some don't make you pay the parking meter, like California, but most do. According to the website, DC allows you to park double the time at a meter, but apparently you still have to pay. I'm not sure if you have to pay for the time that is doubled, but am not sure how else parking attendants would know. But you would know better than I.
https://dmv.dc.gov/service/dmv-disability-tags-and-placards
"Disability parking placards, permits, or tags from DC or any state allow you to:
Park in any parking space designated for a disabled person
Park for double the posted time in any metered spaces (unless prohibited by DDOT's Red Top Meter Program)"