My vote would be against the inclusion of the Imperial March in ANH:R. Personally I find it overused enough in Star Wars stuff as is. The little motif given to the Empire throughout ANH is far better anyway, and doesn’t get enough recognition honestly. I would hate to see it missing from any scenes in the film. Each Star Wars film’s soundtrack generally has its own unique feel to it, at least to me. I associate the Imperial March much more strongly with the later two instalments of the trilogy… Hard to articulate into words exactly, but it just would feel out of place.
I do love the Imperial Theme in ANH, but I have a different preference than you, where I’d rather see it more in TESB and ROTJ. For example, the aforementioned arrival of the Emperor on the Death Star II would be a cool place to reference the original Imperial Theme with a similar time as that used when the Falcon is pulled into the first Death Star!