Your easiest option is going to be a taxi. There are WDW buses to ESPN WWoS, but I believe only from Pop, CBR or All Star Sports. You'd have to get from the Poly to one of those resorts and change buses, plus the buses don't run as frequently as the regular WDW transportation to parks/resorts/DS. We did the bus transportation once and there was a LOT of waiting around for a bus. If I do it again we'll just take a cab. I would assume the cab can put the stroller in the trunk.
Enjoy your vacation!