I missed the posts where it was mentioned that you were about to put it on a credit card (I guess so the interest rate would be 0% on the CC). I didn't see what your current interest rate is. Assuming it's reasonably low, and assuming you were interested in retiring and getting a subsidized ACA plan, that could save you thousands (as much as $10K or $20K per year). As you can see, it could be a LOT more than what you'd save even compared to getting 0% leveraging your credit card to pay down your mortgage bill.
To put it in perspective, I was eligible to continue on my former employer's health care plan (both Cobra and post Cobra). My cost for the 4 of us (myself, spouse, and 2 college aged children) was about $24K for Cobra and $30K post Cobra. Taking the children off would've reduced those about $8K. Health insurance is expensive. This is why a lot of people continue working just for the health insurance.
To answer your question about where to put the extra money, it would be something safe, like short term CD's or a FDIC insured money market account. Something you could tap as needed for expected or unexpected expenses without worrying about the stock market fluctuations. The key to getting ACA subsidies is managing your income so you stay below the ACA subsidy cliff. If you hit the cliff because you need too much income to pay all your bills, you get $0 as your subsidy (and have to repay for the entire year any subsidy they have already given to you).