The trick with insurance is to go into a plan in good health and have it when you get sick. That's kind of tricky sometimes. . . .
Caveat: My experince is in Michigan, so your mileage may vary depending on your state.
If you have a policy that you got before UC was diagnosed, you may be best served by keeping it, even if it stinks. Trying to change the policy may well cause another company to reject your application.
In Michigan, BC/BS is the insurer of last resort, meaning that it cannot deny coverage. You can charge someone an arm and a leg, but it cannot deny coverage.
If you (or a dependant child) is a member of a group policy, it would behoove you to get coverage before the policy expires (or within. . . 90 days). The rules governing coverage change after that grace period and you can be denied coverage. If you have been in a group policy, I believe you must be allowed coverage.
Don't lie on the application. Your coverage can be denied, and you can be fired. That said, in Michigan anyway, there is a time period in which insurance companies must discover that lie. After that, your coverage should be fine. (But who wants that hassle???)
Frankly, though, when I add up what I would have spent on UC and compare it to what I've paid in insurance premiums, I'd have been cheaper off without the insurance. With that in mind, someone with UC might be well served with a major medical policy and a high deductible.