The description in ParkWhiz of the lot 1 Black Falcon Ave says "This location is only used for Cruise Ships that come in on Friday." (and the cruise in question leaves Saturday). I opened a ticket with ParkWhiz to confirm that, and they referred me to the operator of the lot at (617) 482-2487, who confirmed that there is only someone there on Fridays, and there is no automated entry into the lot. So that looks like a no-go.
The official Massport lot 93 Fargo St is $450 ($30/day). I haven't found anything better yet... if you find something, please let me know!