If i understand correctly you play trough a single V30? That would explain the thin part at least compared to the link you gave. The fizzy part can be anything, i think its likely to be the PAF pickups. You can do something about it but youll probably have to noodle a bit longer on the settings. This actually is the oldskool way, PAF>boost>dirty amp, the sound of that is unmistakenly so, if you like that oldskool sound just live with small imperfections (probably noone will ever hear those anyway).
IMVHO thats the bottomline in these matters anyway, you can throw in thousands and just prospone the compromise you have to make anyway, youll be better off compromising now a bit and just enjoy playing, simple.