Figured it out. Thanks for the hint, Gpof - I just sent you a star!
Technical details: I checked the database table where historical records for past months are stored. One tidbit about the game's database is that it stores levels almost nowhere, but rather instead stores exp values and then converts to levels on the fly when they're needed. The historical records table is no exception, so unsurprisingly, I found there were many records from August 2011 and earlier with an exp value of 2,147,483,647, which corresponds to level 114. This number is 2^31-1, which is quite suspicious and (as Gpof said) points at an integer size limitation that was in place at the time. Since the problem wasn't present for the September 2011 records, I looked through commits to the game's codebase during that month. On September 5, 2011, I submitted "Bugfix: Exp values being truncated from using integer instead of double.". That then led me to http://bots4.net/forum/3/2456 which is what prompted me to fix it at the time. Note that that thread talks specifically about profile shadows (i.e. records from when you've reset your bot) - what I failed to mention is that I also fixed the same problem in the end-of-month script.
What's next: This bug suffers from the unfortunate combination of being (a) tedious to fix and (b) low priority, so it'll probably stay as is for awhile. It's tedious to fix because it requires combing through old database backups (and this is still imperfect - they're taken at 12:05am server time each night, so if you gained exp in the last 23 hours and 55 minutes of the month, that information is gone forever). This is also further complicated at the moment by the fact that the hard drive that I have these decade+ old records in is currently in need of repair (fingers crossed). And it's low priority because it doesn't really break anything. For now, I've just added a notice to the historical HoF pages when viewing the affected months with a link to this thread.
Side note: I'm surprised this hadn't been noticed until now (well, 2022). Or maybe it was and I'm forgetting? IIRC in the last days/hours of open beta, I'd cranked up exp rates 1000x or something ("Time of Madness") and a bunch of bots hit level 500+. I would have assumed people found it jarring to not see that reflected in the historical HoF.