Hello Justjeff
I have a Weber 12F150 (C12N) that I tried in my LSS.
The Weber 12F150 is supposed to be a warm speaker, but wow, it really added top end brightness to the LSS. This improved the clean sounds, especially using the neck humbucker of an ES-335. However, the OD and distortion tones were too raspy, almost to the point of "ice pick in the ears." Dropping the treble and presence controls down helped, but the tone started to sound kind of lifeless when I did this.
I e-mailed Ted Weber about this, and he suggested a couple of speakers, among them the Weber Blue Dog (ceramic or alnico versions available), which emulates the Vox Blue from the original AC-30. Note that the new Celestion Blue gets rave reviews, but handles only low wattage and costs an arm and a leg.
I think a California would give you a similar effect to the Weber 12F150, too much brightness for the overdriven tones. In fact, if it sounds like a JBL, it will give you even MORE brightness than the 12F150, more suitable for Surf than Blues.
I ended up with the Eminence Red White & Blues speaker. This sounds just slightly brighter than the C90, and seems to improve the clean sounds and add a little high end to the OD sounds of the LSS without causing raspiness. Eminence has several other speakers, and you could probably choose a slightly brigher one for the LSS without problem, depending on your preferences and rig (pickups, cord length, effects etc.).
Hope this helps.