I think you meant this?
http://www.dspguide.com/CH33.PDF
And, yeah, nevermind that last comment. Of course you can combine a two parallel filters into one by summing their z-transforms. Brains fart from time to time, and mine is no exception.
If you do want to go that route, you're in luck: it's not going to be a fourth-order filter. The reason is that while your tone stage uses two second-order filters, the ones mentioned in the paper are first-order filters. (The patch I posted was really meant to illustrate how to sum [filterplot.mmb]. I just used the [filtercoeff.mmb] for convenience.) Those will, in fact, sum up to be a biquad.
Also, one of the reasons why you might find this distortion so "acid" could be in the guitar sample you've chosen. It really has a lot of highs and sounds like it's had some processing already done to it. I've tried running some dry samples through (sorry, I can't legally share them), and they don't quite have that acidic sound to them.