An update on this.
I have recently purchased some insurance from the insurance branch of Danish healthcare company IHI Bupa.
They will insure you regardless of your nationality, residential status, activity, destination (war zones included) and duration of trip. You can choose both travel insurance and medical insurance in your quote and unlike most medical insurance that will cap the payout, this policy will pay 100% of the cost incurred in most instances.
As a comparison, a single trip policy costs approximately twice that of BMC for example.