Given that the cathode is essentially at RF-ground by virtue of the decoupling capacitor, connecting the SG to the cathode shouldn't be a problem.
Unless you already have an EL84, why not try using a 5763/QV03-12? It's got a separately-connected SG and was designed-from-the-outset as a RF amplifier.
http://www.r-type.org/exhib/aam0048.htm