I recall a report on this board, a year or two ago, from a guy who did the HST and JMT south to north. He may have thrown in Whitney. There is certainly no reason it would not work the other way. It sounds like a great hike.
There is the resupply issue. The southern half of the JMT is the harder one for resupply, and heading from Wallace Creek to the west adds to that. But one faces that challenge in either direction.
I have done the HST east to west. It's a great hike in either direction.