You're quite right; there's far more to do in aviation than fly for an airline. I've done most of it. That said, there aren't very many jobs in aviation that are stable or long term, and that includes the airlines.
Ambulance jobs such as the King Air position you mention tend to be about forty to fifty thousand a year jobs. The companies that do those jobs tend to last a few years and close, get bought out, morph into something else, etc. They rarely, if ever, have any kind of benefits outside of insurance; no retirement, usually no 401K or cafeteria plan, generally no life insurance, etc. Often no dental or vision insurance, either. When you're starting out, fifty grand sounds good but you won't be getting an air ambulance job right away.
In today's climate, you can expect to need about 2,500 hours or more to qualify for an air ambulance job flying a BE20, and more time for something like a BE350. This isn't always the case, but usually so. Corporate jobs and established turbine medevac jobs tend to hire people with more experience. To get insured, you'll need turbine experinece and a solid background that includes some 135 flying, ideally some corporate type flying, instrument skills, and so forth.
Once you get a job like that, don't expect much in the way of pay increases for a long time to come. They're not usually very upwardly mobile jobs. Sometimes you can use those jobs to get into turbojet equipment, if the same company is offering it. A typical transition might be starting in a Navajo, then moving to the BE90 or BE20, then into a Lear or Citation or Twin Commander. To get that far, of course, you'll need to get the requisite time, and you'll always need to keep in mind that it's not the advertised minimums that you'll need, but the competitive ones. That's what it takes to compete with others who want the same position. If other people applying have 5000 hours, for example, then the competitive mins are 5000 hours. It all depends who else is looking for the same job.