Not big enough imo. You are going to need some serious $ to make this work.
The beam you specify would have around 2-1/4" deflection under load in the center as well as being very dangerously close to fail in 36ksi steel. You will not be able to roll the load up out of the valley created. You have to remember that runway rails have to take the entire load if the hoist is placed at either extreme end of the bridge rail. The load never raises smoothly enough to prevent some kind of impact, whether it be chainfall hoist or a powered one.
Aside but related, I calculated the steel needed in my shop for a 25x40 bridge crane 3000lb cap, with 6 posts as I have a hoist with a powered trolley. I got a ballpark of around $5k. This is just for the steel structure. No track, no cable, no controls. Its a large fabrication which needs a careful layout & fabrication to be within about 1/8" of parallel and level. You should design it for L/480 deflection or better and you should use a P.E. which I am not, to approve the design.