EDIT: I solved this, so see below for my own answer. While the bounty asks for a fix to the problem, I'd like to award it to someone who can explain why a cron process that ran for 6 years over multiple MacOS versions suddenly became a problem in Catalina.
First note, this is not a duplicate of "cron" processes piling up because I don't have active crontabs on my computer. Cron processes spawn, but they never finish, so they just keep piling up. I'm running MacOS Catalina 10.15.1
Cron jobs are spawning every couple of minutes and never dying. The oldest cron process always has a parent process "launchd", and I've searched for populated crontabs and can't find any. If I let this go on long enough, eventually I run into a scenario where I have hundreds of running cron processes and everything on my computer grinds to a halt, and I can't even open new apps (I get cryptic messages like ".app cannot be opened" when I try to open an app). My only solution at this point has been to keep activity monitor open and periodically killing off all active cron processes.
I've been able to create a new user account that seems to be immune from this issue. However, as soon as I logged into my apple ID on that account to set up iCloud drive, the problem started with that account, too. I logged out of my Apple ID and attempted uninstall iCloud drive, but the problem persisted. Clean installs of Catalina don't clear up the problem, I've reset SMC and PRAM multiple times, and repairing permissions (via this https://support.apple.com/en-us/HT203538). I've also ensured that cron has full disk access (via this https://blog.bejarano.io/fixing-cron-jobs-in-mojave/). I'm at a dead end with trying to troubleshoot this problem.
I'm not sure it's related, but my "system.log" file seems to get spammed the following few lines:
<redacted> AMPDeviceDiscoveryAgent: Entered:_AMMuxedDeviceDisconnected, mux-device:63
<redacted> AMPDeviceDiscoveryAgent: Entered:__thr_AMMuxedDeviceDisconnected, mux-device:63
<redacted> AMPDeviceDiscoveryAgent: tid:9a27 - Mux ID not found in mapping dictionary
ANY help is appreciated.