If you read the regs, you will find that all turbojets require an SIC. I am not completely knowlegeable about Citation Ops. never having operated one, but it is my understanding that some Citations can be operated single pilot, but only if certain criteria are met. The aircraft has to be configured for single-pilot operation, with all required items operational, and the pilot has to be authorized to operate single pilot, and must be current as a single-pilot operator,which is different than being current for two-pilot operation.
Regardless, I believe that the PIC can decide whether or not to utilize the SP provision. I know that I wouldn't. Single-pilot Ops have a incident/accident rate that is 35% worse than two-pilot operations, which is why insurance companies tend to prefer two-pilot ops.
As for your question about how "airlines" feel about Part 91 jet SIC time?
Well, when I had 1500tt/300MEL (all piston), I couldn't get anyone to interview me in 1997. After I got 300 hours of jet SIC time, I had interview offers from PSA, Allegheny, COEX, TSA and others. I turned them down for a good 135/91 co-capt job, got my type, became a 135 Capt., and the rest is history. Oh, yeah,
made very good money in corporate and got good jet experience.
Good luck, but don't think that a regional is the only game in town. And buying right seat time? Well, fuggedaboudit.