Genera Reso's are quite similar to G1's but with a slightly brighter tone and a bit more lively overall.
I currently use them under Coated G2s on my Starclassic W/B and love the sound, although they are not the short/mid sustain OP is looking for.
For what its worth, I use Coated G2s over Clear G12s on one of my other kits; a Starclassic Maple.
The sound is fatter and more punchy, with a notable emphasis on the low/low-mid frequencies.
Technically a thicker resonant head should produce more sustain, and it does, but the tone is focused to the point where that extra sustain is basically inaudible in the context of playing the full kit.
Mind you, this setup works for me on Maple drums where the brighter tone of the shell combined with the darker head combo, gives a sound that is relatively balanced.
Not sure how the same head combo would go on a darker sounding drum like the W/B (hence why I selected the Genera Resos for that kit).