Denied based on medical condition. Any other options?

I recently applied for life insurance and was denied. I went through Geico (whatever 3rd party they use) since that’s where my car and homeowners is held. I was told they reached out to a large number of insurance companies and all denied me. I have an extremely rare congenital condition called Osteogenesis Imperfecta, which results in brittle bones (Samuel L Jackson’s Mr. Glass character in Unbreakable had OI 😆). There are varying degrees of the condition and I have the most mild type, which has been confirmed via genetic testing. I’ve broken ~40 bones and it’s a pain in the ass, but it has no affect on life expectancy at all. Though obviously if I were to be in a serious accident there’s a higher risk of death. I am 36 and otherwise completely healthy. I was really surprised by the full out denial and wonder if it’s because the condition is generally pretty unheard of and quick searches can bring up some scary results. The more severe types can be very severe – breaking a bone when you sneeze or roll over in bed, not surviving past infancy, etc. I’ve often had to explain the condition to doctors and even a lot of Orthopedists have never met someone with OI, so I would be surprised if an underwriter was familiar with the nuances of the condition. I was never asked any specifics about my condition beyond the name and brief description.

I do have life insurance through my employer, but I’m unable to increase it and would like more than I have. What can I do? Is there a company that might entertain insuring me? What if I submit the genetic testing that shows the degree of the condition? The location and type of genetic mutation definitively shows the type of OI I have, so it’s not a matter of it being a clinical diagnosis based on a particular doctor’s opinion or anything like that. When I was denied the agent working with me didn’t have any ideas of where I could go from here. Maybe nowhere? I have a 5 year old and am just concerned with having enough set aside for him. My only other idea would be to get a large insurance policy on my husband so that if we died at the same time his policy would compensate for me as well 🥴