IMHO, you are correct in that overhead transmission lines do act as antennae and pick up high voltage pulses that are apt to destroy both the equipment connected to the line, and possibly the overhead line itself.
A buried HVDC line should be far less vulnerable. Unfortunately though, the power to be fed into this new HVDC line still has to be produced, and virtually all power plants of significant capacity are above ground and therefore very vulnerable. The converting plant to turn relatively low AC voltages into the high voltage DC is also large and vulnerable, and for reasons of both space and cooling is invariably above ground.
It might be possible to bury both whole power plant and the converting equipment, but the costs would be vast, and the complications regarding cooling would be undesirable.

That still leaves the other end of the HVDC link. The converting plant is bulky and vulnerable, and the electricity once converted back into AC will be fed into the existing above ground network, none of which is protected against EMP.

Electricity post an EMP event is likely to be on a very small scale from portable generators, PV modules, and vehicles that were stored by luck or by design either below ground or in a well shielded building.