Given the stuff I've seen people schlep on to local trains in Japan, I'd say you can still make it without going for green cars and shinkansen and such for this 35-40 minute (max) ride. It would not be a quality experience during morning rush hour, but even then it is probably doable.
If you don't need ALL your bags the same day, a takyubbin service will deliver them hotel-hotel for a reasonable price overnight -- admittedly, most wouldn't use them for a trip this short, but for comfort, it sure can't be beat for Y3,000-4,000 or so, and the hotels at both ends will take care of everything for you, so you don't have to bother at all.