The central Providence part of your map is problematic. You can't have a rail line turn 90 degrees within Downcity, since the minimum curve radius for mainline rail would require widespread demolitions. It would only work if you're proposing to run a tram-train, operating in streetcar mode in Downcity.
It's actually really hard to connect the East Side Rail Tunnel to the existing tracks to the north and west of the city. When the elevated tracks serving Union Station were demolished and the station moved to the north, the connection to the tunnel was severed. It is also very hard to serve Providence Station from the tunnel, unless you make unconscionable compromises on curve radius. It might have to be put in the "too hard" basket for the next few decades.
If you want everything to connect, you have to move the tracks back, which means closing Providence Station, or downgrading it to a secondary station, and building an elevated station above either Kennedy Plaza (more central) or Memorial Boulevard (easier). Such a station would connect. The problem: els aren't popular, and to allow reasonable throughput the junction to the east of the station, with lines to the tunnel and toward Pawtucket and Woonsocket, would have to be grade-separated, increasing visual impact. The main saving grace is that the required demolitions are cheap, and the new construction would allow high enough curve radius that squeal would not be a problem.
See
this map of options. Memorial requires losing Citizens Plaza, which was bought for $60 million in 2005; this is a significant fraction of the likely cost of building the viaducts in Downcity and digging a station at College Hill, but still just a fraction. Kennedy Plaza requires losing a small building housing three restaurants, but the construction costs and impacts in Downcity are likely much larger, and the station would be on a sharper curve.