Or you could probably just park on street in the seaport/world trade center area.
You can't be serious about that. Parking in that area is challenging at best-a truck and trailer for someone who might not be experienced in that area is not a good idea.
I believe his line of thinking is to NOT drag the trailer into Boston. Yes, people do it especially when it's back-to-college time but it doesn't make for a fun time.
Of course your rig won't be much bigger than the u-haul/ryder truck rentals that get double parked all over town before labor day, so you might be able to just blend in.
You're not suggesting he double-park, are you? Great way to get towed and make more problems.
I think the OP could find a Walmart,supermarket,mall parking lot, with access to the the T, and be good to go.
This is probably the best thing to do. Again, if we know how the OP is passing Boston, that would help.