[Arran]

 If the original transformer is actually shot just treat it as an AC/DC set but with a power transformer for the B+ using a 50X6 as a full wave rectifier. Or you could forget about the transformer entirely and use the 50X6 rectifier in a full wave voltage doubler circuit from a Philco 46-1201. One thing to keep in mind are the maximum ratings of the 50X6 and the 35L6/5OL6 if you go the transformer route, the typical 350-0-350 style of high voltage winding is way too much, I think that 180 volts is the maximum.
 The only logical reasons I can figure for why they designed this set the way they did was because they either got a good deal on some 25L6s and 6X5s or they couldn't get their hands on some 50L6s, other then that it would have been due to the whim of the engineers at Stewart Warner. The only thing that I have seen stranger then this was some of the brand Z and G.E sets that used an autotransformer, most of the AC sets that I have seen with the tubes in a series string arrangement used the transformer for isolation of the B+ side  and to give the power output stage a bit of a boost.
Regards
Arran