It sounds like great fun until your rapid transit pod plunges into a bath of superheated magma. Vomitous fellow passengers would not be my primary anxiety about this mode of travel.
If you don't go too deep (a few thousand KM), the temperature is under 1000 degrees. We have plenty of materials than can handle that. For insulation use vacuum, or aerogel (which melts at 1,473 K) and is a phenomenal insulator. Add a large cold reservoir (liquid nitrogen) and you don't need a conventional A/C - it only has to last 42 minutes, and weight is not a problem.
The pressure is a much bigger problem. You can't bore a tunnel in the conventional sense since the rock is a liquid. You'd need some sort of wall, but I don't know if we have anything strong (and stable) enough. Most metals will oxidize and destroy themself at those temperatures.
Maybe a ceramic, or alumina coated metal. Perhaps a tungsten compound of some sort that is stable in oxygen at high temperature.
Another problem is the speed (reaching 1000 MPH), you'd need magnetic bearings (mag-lev), but magnets don't like being hot. The curie point of iron is 768 C, which is too low. Cobalt might work - but barely.
Also, I wouldn't want to build something where a single seal failure would mean the entire thing is destroyed. Plus, how would you construct it.
And if you survived the crash - how would you get out? The capsule is unpowered, and they don't make cables long and strong enough to pull you out.
But assuming rescue was possible, I suppose they could drop small emergency coolant refill bags down to you.
Anyway, it's nice to see he solved the pathfinding, but it's probably not the most challenging part of the problem!