Have you thought about SelectQuote? They actually work for maybe a couple dozen insurers. You apply and they find the best rate for you. The insurer pays them a fee for directing the business to them. I would think one of these companies might work out for you.
The whole thing sounds pretty weird to me. I just got 30 year term insurance. I told them I used to smoke, smoked weed, and that my dad died of cancer when he was 49. I got passed as a "preferred" member with USAA. Granted, my bloodwork came back fine, so that is a big bonus, but my point is that each company is different so you might consider just cutting your loses and moving on.
FYI, all life insurance companies ask if you have ever applied for life insurance previously and been rejected. Lying would not do you any favors. Explaining to them the situation would probably clear it up...
Just my opinion. Good luck!
"...I'm the kind of guy who if he can't have too much of a thing doesn't want any at all."