I was wondering about the Starfire XII lately. I'm kind of surprised to hear that yours isn't sounding good to you. Does it have the smaller humbuckers, or the full sized ones ? The smaller ones, I would think would be preferable on a 12 if you're going for chime, because they are a bit brighter.
I'm kind of into Rickenbackers. The old toaster pickups are simple single coil designs, not particularly high output, and they are important to the sound. But also, the neck joint and bridge make big contributions. In both cases they are not optimized for sustain, strength, or reliability, but they have a way of de emphasizing mids and adding harmonics and resonance in the high frequencies. That bridge especially is cheesy, since the only way the energy can get transferred from the strings to the top is through the 4 screws, in the corners of the bridge, and the other end of each screw isn't even touching the top of the guitar, they just stand on the metal plate which is in turn screwed to the top. Usually, they aren't all making even contact to the bridge mounting plate, because you want a little angle on the bridge, which further contributes to the controlled chaos. The whole effect is kind of like, halfway between a tele bridge, and one of those Danelecto sitar "buzz" bridges !
They also use a high pass cap on the bridge pickup (or at least the old ones and vintage reissues do), to further cut lows as long as you're using the bridge pickup, or both of them.
In conclusion I think it is nearly impossible to nail a Ric 12 sound without the frustrating but crucial Ric bridge. On the other hand I have a Danelectro 12 with an aftermarket all metal adjustable bridge, a high pass cap on the bridge pickup, and more vintage correct lipstick pickups in RW/RP configuration, and a blend knob replacing the switch; I got the thing in this modded state for a grand total of $150 (!) and it's as close as I've heard to a Ric that isn't a Ric. I think the metal nut on the Dano helps it get into Ric territory.