Superhooper,
An underwriter is looking for any condition which could reduce life expectancy.
No point sending a clatter of applications to different insurers you'll be only wasting everyones time. Most of them share the same reinsurers anyway. What you need to do is go to your intermediary (who should have a wide range insurance agencies - if she or he doesn't then don't touch him/her with a barge pole) with a page where you have written as full and complete a history of your medical complaint as you can. Ask your intermediary to use his or her experience and to have a chat with the chief underwriter for an opinion as to the likely outcome of submitting an application. If you get a positive or encouraging response then submit a full application.
By the way superhooper try not to don't get down in the dumps about a refusal to insure. From my experience the creaking door definitely lasts the longest. It's the ones that are as fit as a fiddle who drop first.
Wishing you all the best,
Sumatra