Is there a realistic fix? That's a question many people have been asking for a long time, without easy answers. If the New Haven Line is the NEC's Achilles Heel, then the portion of the line between Stamford and New Haven is the Achilles Tendon of the Achilles Heel. Between NYP and Stamford there are multiple challenges, yes, but many of them are fixable without carving out an entirely new alignment, but between Stamford and New Haven you have, among other challenges, the sharp curves around Darien and Norton Heights that would require knocking down entire neighborhoods or multiple miles of tunneling to improve, the 45-mph WALK bridge (whose alignment through South Norwalk is basically impossible to improve), and the 30-mph Jenkin's Curve just south of Bridgeport (basically impossible to rectify without either knocking down downtown Bridgeport or tunneling under the downtown and Bridgeport harbor). The portion between New York and Stamford, though, can be improved with a few projects, and could make Amtrak competitive and enable 2.5-3 hr New York-Boston travel times.
In the Bronx, sharp curves at Hunts Point Ave.-Bruckner Blvd. and Westchester Ave.-Bronx River can be eased to 1.6° with a few takings (one of these would involve replacing Starlight Park). There's also an S-Curve near Morris Park further north in the Bronx, but it can be eased with minimal takings to 1.6° (mostly parking lots) and isn't fatally slow in its current form. The Pelham Bay Bridge needs to be replaced and its curvature should be reduced to 1°, but this is planned anyway with the Metro-North Penn Station Access Project. With those improvements and a re-alignment to 2° near CP Gate in Queens, the entire Hell Gate line would be good for 100-110 mph for Acelas, excepting the sharp curve on the Hell Gate Bridge.
The problem with the New Haven Line between New Rochelle and Stamford, even more than the curves and the flat junction at SHELL Interlocking, is how busy and congested the line is. There is a solution, though, that could help Metro-North and Amtrak. Today the New Haven Line has four tracks, but it was built for six from New Rochelle to Stamford. (The fifth and sixth track were used by the New York, Westchester, & Boston during its existence from Larchmont-Port Chester). I-95 has encroached on the six-track ROW in Larchmont, which will require some unpleasant takings to restore, but if Amtrak had its own dedicated two tracks, it could dramatically increases service levels and increase speeds (many Metro North trains terminate in Stamford, so the line between Stamford and New Haven sees less traffic). The alignment is not the ex-PRR and has a few 2° curves in addition to a few painfully tight twists and turns (around which Amtrak should construct bypasses on I-95), but Amtrak could offer service that is unimaginable today sharing trackage with MNRR. Giving Amtrak its own two tracks also eliminates the problem at SHELL, where a dive-under or jump-over for Hell Gate trains has proven extremely difficult to construct. If an extra station track were built at New Rochelle (it currently has 5), Amtrak could use the two southernmost tracks of the 6-track ROW, eliminating the need to cross MNRR trackage. Amtrak should also use that project to ease the S-curve on the Hell Gate line leading to Shell (this would require taking about 20 properties). Routing Amtrak on the southernmost tracks would require moving station platforms at Larchmont, Mamaroneck, and Rye, but hey, nobody said this was going to be easy.
Once past Rye, 3 sharp curves remain at Port Chester, Greenwich, and Cos Cob. To bypass the Port Chester curve, Amtrak would have to construct a bypass following I-95 to Greenwich. Once past the Greenwich S-Curve, there is ample room for a flying junction for Amtrak trains to transition back to the central express tracks of the 6-track ROW. At that point the only impediment to nonstop 100-mph running to Stamford is the Cos Cob Bridge, which sits between two sharp curves. Replacing the bridge with twin curved, 3-track spans would allow 100-mph speeds and continue Amtrak's segregation from MNRR traffic.
So... is this fixable? Yes, but it would be a herculean project to even improve the half of the line that is easier to fix! For what it's worth, Amtrak's published plans have been even more aggressive, planning to construct an entirely separate 2-track ROW following I-95 between New Rochelle and Stamford. We shall see what of any of this comes to pass, but although many say the meek shall inherit the Earth, I have always believed that the world (or at least internet forum posts) belongs to the bold.