I tried a few things, and it appears that the only thing to stop the battery level from plummeting is a reboot. Cycling Wifi off and back on seems to help a little, but not completely.
As far as the 0x886c packets go, they appeared roughly once every second in a pcap sample taken shortly after the first "Returned to Wifi".
A few minutes after "Rebooted Phone", I saw a flurry of about 10 of them in less than a second. Random 1-2 minutes samples during the next hour or two showed an occasional 0x886c packet -- maybe 1-2 per minute.
I didn't see any 0x886c packets in samples taken immediately after the second "Returned to Wifi", "Cycle Wifi", "Cycle Data Network Mode", or "Cycle Flight Mode".