I can see that you may get a discount for leaving your car in an armed forces car park as that is likely to be a patrolled and secure area and theft, break in etc. is less likely.
Often the problem of denial of insurance or strict limitations doesn't come from the up front insurer but from the up front insurer's
re-insurers. All underwriters and companies will take on risks and they then buy layers of re-insurance from re-insurance companies to cover themselves. Re-insurance companies are strictly financial institutions staffed by financial gnomes who's only skill is reading a balance sheet, they work in offices far removed from reality or, in some cases, mankind.
I would always recommend that you find yourself a LLoyd's approved broker who has access to the entire market, including special risks. The underwriter pays the broker, not the customer, so insuring via a broker should not cost you any more, a bit like credit cards, they do cost the vendor but it is considered worth it to secure the business.