Doug, according, to
www.insuremytrip.com, Travel Insured (Worldwide Trip Protector Gold) does not cover pre-existing conditions unless purchased within 10 days of original booking.
Ngaire, only options I can find on
www.insuremytrip.com except CSA freestyle luxe that cover pre-existing at final payment is HTH Worldwide. Otherwise, I think you are going to need to find a company (can't tell from insure my trip) that lets you assign premium to future trip if you cancel between deposit and final payment. This isn't the best of all possible worlds but it will be most cost effective for those with pre-existing conditions.