Don't know much about this specifically from the employer's point of view, but I know health insurance pretty well so I'll chime in:
first of all, it wouldn't cost your employer 5K + premiums, it would cost them either 5K if they're self insured (larger than ~2,000 employees) OR premiums (which may or may not increase for them because of your inclusion on the plan, it depends on the size your employer). If you have a large employer, there is very little chance that they'll ever know how much you're costing them.
secondly, 6K per year is actually not a particularly high cost person, it's actually pretty close the average, so you're not as big a risk as you think (unless your CC puts you at higher risk for a severe incident).
Given those things, if you work at a small office of healthy [healthy in this context= mostly young men] people, there's some chance you'll increase their cost significantly enough to notice, and the timing of it will make them know it's your fault. Otherwise, you're probably fine using the insurance for your care.
As for plan choice, you sounds like you have a pretty stable spend every year, so you should be able to sit down with the numbers and plan designs and figure out how much each plan will cost/save you each year.
