The best way to build such a structure would be to fabricate it on the surface, as a long pipe, while simultaneously boring anchors into the seabed. The pipe would be towed over to the site, and winched down into position (attached to the anchors, obviously), which would be maybe a couple of hundred feet (out of harm’s way in a shipping lane) under the surface, bypassing the tunnelling problems, giving more leeway for the route, and getting it done much faster. Such a method could link several locations on each side for vehicular traffic to the main trunk line.
Of course, auto traffic would mean this beeotch would be exploded within days or weeks of its opening, but this approach wouldn’t prevent it from being a train tunnel, so maybe it would make sense to stick with that.