I was going to say that the last time Hyde Park station was closed, trains stopped at the rarely used NEC platforms at Readville. The only problem with that though is tracks 1 and 3 don't merge until just past the platforms, and I believe this is part of the Read interlocking (Which primarily serves as the branch off point for Franklin trains, but is also where the Midland route rejoins the NEC and the other branch merges with the NEC spur and continues to franklin.
I have seen the wooden planks used in the past for something like this at Hyde Park, and I imagine something similar would be done here. The tracks are double signaled so they could theoretically run some outbound trains on track 2, but the last crossover before the station is Forest interlocking, right near Forest Hills, but it would only be a two block stretch that would be affected. Fairmount station is not far as you mentioned. The other thing to note is the 32 bus serves Cleary Square, right near the station, and not to turn this into a bus thread, but the 32 bus is one of the most heavily traveled bus routes in the entire MBTA system, with direct connections to the Orange Line. So there are plenty of options anyways, even if Hyde Park (Which does see somewhat decent ridership, but its in need of repair being 20 years old now) is shut down for a couple of days.
Rich "Dino" Martin
A one time happy rider of Arborway and the old Washington St. El.