The thought of passenger trains running via GJ is interesting. I happened to be looking at some old maps of the area since my mom's family came from there and I was looking at the property. I noticed that the area once hosted not just 1 track or 2, but up to seven in some places. Binney Street even had a substantial freight yard in its early days. Now if we think about it, we have now yet again another wasted piece of decent rail infrastructure that is yet again still under utilized.
Now my thinking for any kind of rail passenger service, we would want to implement upgrades of some kind for the track. Continuous welded rail is a given. If the line is to be upgraded to current standards, and track has to be replaced, why not do this. It's not like it's already 132lb rail anyway, or at least I don't think it is since I haven't been down there in ages in person. Rail crossings would have to be replaced or eliminated as a given to bring the line up to current standards. New fencing with bardbed wire top would be important to keep the line from becoming a short-cut, and to eliminate the current short-cuts along the way.
The same goes with track reconfiguration. This is again a given since a connection would need to be built to connect to the Fitchburg line, or bring the line into one of the many currently abandoned lines in the NS yards. The Beacon Park area would need some work too as mentioned, Soldier's Field Road grassway could easily be used for this.
The ride may only be 20-30 mph along the length. So what... It's still a continuous 30 mph starting from Beacon Park or thereabouts and running to North Station yards. This is unlike stopping, getting off the train, walking to a T station, and then waiting for another vehicle running along. The continuous ride is somewhat faster because there is no lag time with the stopping and starting.