There is an unresolved problem with the equivalence principle. Acceleration thought experiments do not involve any curvature of spacetime. As far as I know all explanations of gravitational time dilation do.
This does not necessarily invalidate the equivalence principle. It merely says that something somewhere is not right.
The direct observation of gravitational time dilation matching that expected from Special Relativity thought experiments in flat spacetime suggests the 'something somewhere' might not be the equivalence principle.
The flat space acceleration thought experiments (accepting the clock hypothesis) say that clocks a chosen distance ahead (in the direction of acceleration, distance measured in a momentarily co-moving frame) are judged to have an absolute addition to their rate proportional to both the acceleration and the distance, without limit. Looking behind, they have an absolute subtraction, again without limit, so that beyond the clocks judged to be stopped there are further clocks judged to be running backwards. These additions and subtractions apply both to co-moving (accelerating) clocks and to clocks in any rest frame the momentarily co-moving inertial frame is compared with.
The equivalence principle can only be tested over a limited gravitational distance for practical reasons. There is an issue, however, since the gravitational effect is not proportional to distance without limit when the distant clock is in a distant rest frame.
It seems unlikely the issue is with the clock hypothesis or the equivalence principle. I suspect it is more fundamental. (the work is ongoing)