I apologize for not reading the documentation closer, the answer was right in there
Kinda buried, but I found it. I deleted the last backup chain and as documented, the next scheduled backup was done as a full backup to start a new chain. Success! I'm a bit confused as to why the backup is still in the Veeam Agent control panel, and just for fun I clicked the "restore files" button (it is a Volume level backup) and when the Backup Browser came up I got an error "some errors occurred. See log files for additional info". After some searching and digging I found a log file (buried in C:\ProgramData\Veeam\Endpoint\FLRSessions\Windows) with an error:
Opening storage [\\<my server>\Backup\Backup Job xyz\Backup Job xyz2018-07-10T022205.vib] in read-only mode. Failed.
Which makes perfect sense since of course it is not there, that's the one I deleted.
I guess it makes sense that the deleted backup still shows up in the list of restore points... if those missing files were to, say, suddenly re-appear, everything would be fine. Doesn't look like a problem to me, since I was able to open up the full backup created after the manual deletion with no problems, so I'm good.