Sputtery (gated? that's kinda the opposite of sustain) makes me think voltage starve. Not sure if I'm taking "sputtery" to mean the same thing you do though - maybe I'm thinking "splatty." Are they synonyms?
Talking about dirt sounds is almost as bewilderingly abstract as describing wine - "glassy, with a woody aftertaste and a subtle hint of diode clipping".
One easy/cheap idear might be the danelectrode power supply, just throw it on a fuzz or dirtbox you already have. Voodoo Labs PP2+ can starve too if you are already using that.
I have a Mellowtone Wolf Computer (IIRC a boosted silicon fuzzface at heart) and it has a voltage starve pot right on the top along with a "squelch" control for gating, which one might think of as an "anti-sustain". A truly wild and unruly fuzz, and touchy, very sensitive to slight tweaking and guitar volume/tone, especially when starved. Lots of gnarly, amp-exploding, velcro sounds in it. Fun!