After launch you’re going to want to rapidly gain altitude as fast as the passengers can tolerate (so ~3g), but even if you lose 30-50% of the input energy your still dramatically reducing your on board fuel needs as in ~30+ seconds of main engine burn.

More importantly you can have an air breathing sage without including a sub sonic air breathing engine which vastly simplifies your design. Further, one proposal was instead of trying to accelerate using an air breathing engine you simply try and maintain velocity as you gain altitude which further expands your useful design space.

Net result, reusable single stage to orbit, with a useful mass fraction, might be possible. Though, I agree trying to hit mach 4 near sea level is going to be a major design issue. But, Mach 2 is defiantly possible and probably a better first goal.

And you're right, I did misread what you had written earlier. Thanks for engaging rather than downvoting.

As to vertical track, you might be able to build a 2 mile near vertical track but you end up adding a lot of energy more cheaply with a horizontal track and for the most part it's energy that's important as you can trade horizontal energy for vertical energy inside the atmosphere. Don't forget for moderate cost you could use balloons to get a few tons to 50+km up where the air is vary thin. But altitude is just not that much of an issue.