that's a tricky one as far as advice to give you on a dedicated CA route truck. Out of state guys go in there with non-compliant trucks from what I understand...not really sure what risks or penalties they are subjecting themselves to, if any. I know they have clamped down harder on Class 4+ trucks and companies registered in CA, but that's different. I'd advise you to ask the owner op section as well.
The biggest question besides that is the insurance, especially with it being a 3 axle tractor with a high GVWR. You'd have to talk to your insurance company about it. The F-750 and 5500 are considered commercial vehicles also by insurance but since they are are 2-axle and don't necessarily require a CDL to drive as company vehicles there might be an issue there.