Now, you're thinking! Of the tubed distortion effects I've seen, many have used the 12AX7 to just add a high gain stage in front of the input to the amp. Sometimes with some passive EQ to boost high freqs more.
You won't need much in the way of current for the B+ with this approach. Two small 120V:12V tranny's would do it. 120VAC to the 120VAC primary of tranny one; 12VAC from secondary of tranny one to 12VAC secondary of tranny two; at this junction, take 12VAC to run the filament, from the primary of tranny 2, you will get 120VAC which you can rectify and filter for B+. Use a voltage doubler if you want a bunch.
You get the transformer isolation this way, without hunting up a "special" transformer.
Alternatively, the little transformer from a Foreplay 2 would also do nicely for a little one tube circuit of this variety.
If I run across a schematic, I will try to post it in this thread; the input stage of most 60s Fenders could also give you some ideas.