[ClumsyPilot]

"While I don't know of any washers/dryers with them, heat pumps can be more than 200% efficient"

But then the washer is stealing heat from your house? That seems questionable?

Seems like the right way to solve the problem is to provide hot water inlet, and that should provide it is whatever most efficient way you can?

[maxerickson]

Heat pump dryers don't exhaust air to the outside, which saves a lot of energy relative to what is pulled from the house.

(The water is either collected in a container or goes down a drain)

For modern top loading washers, the final temperature of the water is restricted by limiting the hot water let in, they don't have a heater.