It looks like your lathe has a bolt-thru flange mount so to put a different chuck you need one with that same mounting style- I would ask Woodstock if they sell extra spare backplates or if you need to buy a complete chuck from them.
Alternately, one could also fabricate your own back plate from scratch and buy an inexpensive 4-jaw chuck to go with it (such as Shars)
Seems like that would be an easier project than making a backplate for a threaded-spindle lathe, but I could be wrong
mark
ps the flange mount you have is an advantage in that you can reverse without worrying about the chuck coming loose, although the lathe may not be capable of reversing the way it's currently wired
pss don't buy a 4-jaw scroll chuck- only useful for a narrow range of work- get an independent