Larkin for pointing out the wisdom in purchasing travel insurance before embarking on a trip. By definition an accident is never *planned". And most travelers won't have the choice or the presence of mind to choose which hospital will treat them. For most travelers the cost of travel insurance is a small fraction of ones travel budget. Here's wishing your wife a full recovery from her injury.
I don't know if the system is sophisticated enough to track your IP address, but the requirement is that one apples from ones home of record (in your case, the US). You can most certainly complete the application from Cambodia and it's possible a VPN will shield your location but with a non-refundable $200 fee you might hesitate at taking a chance.
If your country of residence is in the UK you must apply from there. And the amount will have to have been in your UK bank account for the past 6 months. Once the visa has been approved you can spend it as you wish.