This is an oldie
The first Fulltone Fat Boost was almost a carbon copy of
Orman's Minibooster,
see here. Fuller only added a guitar volume pot on the input of the effect - silly because you already paid for one in your guitar

- same for the tone control at the end. That's why I would still not be more than a Minibooster
But there are Russian occurences of this type of circuit for fets from before Orman's Mini, and in fact it's just tube technology applied to fets, as you can all read
here
When Paul Cochrane published his Fat Bastard mods on diystompboxes.com, Fuller jumped on the design and even included Paul's ad lib suggestion of an output buffer in the
Fulltone Fat Boost V2
So I think it would be more useful to work on the basis of either the crude minibooster or the Fat Bastard, for which PaulC has supplied some hints for improvements in
this thread.