So in three years I'm going to lose Tricare and be back in the civilian job market. It's my understanding that this will require me to enroll in universal healthcare. While I have no problems paying for it, I have my reasons for preferring not to use it myself. Is it possible to opt out of the program in that way?
Your 'understanding' is wrong.
First, there is no such thing as Obama 'care,' it exists as neither a health insurance entity nor a healthcare provider – consequently there is nothing to 'opt out' from.
Second, there is no such thing as 'universal' healthcare.
Third, the only question is whether one will be required to pay the tax to fund the subsidiaries or not.
If one has employer provided insurance or insurance of his own that meets or exceeds the ACA's requirements, he doesn't pay the tax.
If one has a private health insurance policy acquired from the ACA's marketplace, he doesn't pay the tax.
If one is enrolled in his state's Medicaid, he doesn't pay the tax.
If one lives in a state that didn't expand Medicaid, where he can't afford health insurance, he doesn't pay the tax.
If one can afford health insurance but for some reason decided not to buy health insurance and go without, he'll be required to pay the tax.
And if one has a health insurance policy that doesn't meet the ACA's requirements, he'll be required to pay the tax.
Last, those eligible for Medicare are subject to neither the requirements of the ACA nor subject to the tax.