I've just tried to insert a YTX7 battery into the 350 battery tray and it will not fit. It's too wide (2.7" as opposed to 2.36", or 70mm as opposed to 60mm if you think in metric)
One option that I do know of is the Motydesign lightweight batteries (
http://www.motydesign.com/4cell_prod.php). I would imagine that the 4-cell battery would be fine for a Bridgestone, even though it is only 2.5Ah vs. 5Ah for the 12N54B. It might be an idea to replace the standard selenium rectifier with a modern solid state reg/rec to ensure that the battery gets plenty of charge, alternatively Motydesign also do a larger 8-cell battery.
I'm sure there are plenty of other lightweight sealed batteries out there.
Replacement batteries that are smaller than the battery box aren't a problem, as you can easily pack the battery in with lightweight packing material like styrofoam or balsa.