Citation SP ops and insurance issues.
I flew a 550 SP for about two years. Very easy airplane for one pilot, about as basic as you can get and easier than a King Air with one failed.
The 500 type does cover you for SP ops on the SP designated airplanes, but there are not many 550 SP's left since you take a weight hit as mentioned above.
The waiver is a second checkride after the type that must be done in the airplane. Straight forward not a big deal. The waiver is good for 12 months and must be renewed each year. Adds about 1000 to 1500 a year in training costs. After the initial SP waiver, all the renewals can be done 100% in the sim.
Insurance can be had pretty easy, if you have some good time. I had zero Citation time and was covered for SP ops with no IOE (babysitting) required. However I did have about 1400 hours of 737 time prior to it. SP ops added $9000 to our insurance a year.
Total cost on insurance the last year I flew it was 39k plus some change on a Bravo(Older CII would probably be cheaper since our hull was insured for 4.3 mill.) The average King air on our field ran about 28 to 31k a year. So you will pay a bit more for SP stuff.
SP ops will limit you to 50 million in liability, the insurance companies do not like to go above that for SP ops.
Operationally you are limited to 35000 feet unless you go on the mask. Not a big issue, If I needed higher I would hit the mask until I jumped whatever weather was out there. On an older CII it would be less of an issue since it's climb and altitude performance is not as good as the Bravo. 350 is probably about the highest you would get anyhow for a 400 mile trip as you said.
The 550 will do almost every airport that a King air will. I cannot give you a fuel burn for the older twos, but on a Bravo it is within about 5 to 8% of what a KA 200 does if you run optimum profiles for a given route. It burns more but gets there faster so not too much difference. If you stay low though you will burn lots more just like any jet.
Maint. is pretty straight forward, I never had any big issues with ours. About the same money per year as similar sized turboprops that I have flown.
If you live in a hot state, opt for the Freon Airconditioner. The ACM is a little weak on the ground in the summer, so it is nice to have the AUX air for that. (Most 550's have it, I only saw a few that didn't)