I hate to say it, but I might be seconding your broker. While you might not be denied out of hand for private coverage, the companies can easily make it prohibitively expensive for you to maintain it. Employer-based plans usually try to keeps costs uniform across the board for their employees. I'd say take the LTD through your employer and run with it.

I will grant my response is based more on navigating the health insurance market and the similarities to your experience . I don't have much in-depth knowledge on the particular policies you're looking into unfortunately.

Hope that helps somewhat!

Luck!