This problem was solved by China as far back as the DF21D no? Hence why they are guided missiles with CEC despite having plasma sheath.
Plasma sheathing is not an issue to a hypersonic vehicle when a suitable array is available and in position to communicate through the space side of the vehicle. In fact, PLA scientists think Beidou's SMS function is sufficient for guidance.
In March 2005 there was a flight test of a Trident II D5 MARV. The admiral involved in the test claimed "I had GPS signal all the way down and could steer it.” p.40 here:
Now this is a different sort of test but you get the idea.
There are still a couple of hard problems to solve (see 2021 FOBS test accuracy for reference), namely how to make a terminal guidance system that can survive being destroyed by atmospheric ablation just long enough while retaining sufficient precision of control to hit the target with the sort of CEP values that enables prompt global strike. It is an exotic materials science problem.