Brokers and members of Lloyd's of London pride themselves on insuring anything insurable (so not normally against events that have already occurred). They have for example insured Jimmy Durante's nose, Keith Richards' fingers and Holly Madison's breasts.
So if every other avenue turns out to be a dead end, contact an insurance broker and it is very likely that something suitable could be arranged, for a fee.
Selecting your own insurance company may however be cheaper. The UK consumer magazine Which? undertook a survey (based on April 2016 premia, an update is due in November 2016) and they include many companies prepared to provide travel insurance cover that (a) includes USA and (b) provides for "at least £2 million of medical cover for Europe and £5 million worldwide". Since Which? has separately categorised trips of up to 24 days I presume "annual trip" may allow longer than 24 days at a time, but that should definitely be checked as many policies will not cover a long but single trip.
Some of the above cover individuals aged over 80 years, of which some cover those over 85 years. I am not sure how nationality may affect coverage/premia but recognise that at least one of the insurers is part of a group that claims "We are a global insurance company with presence in 49 countries across all the five continents".
It happens I have also seen the site (with a .co.uk domain) for AllClear Travel Insurance which mentions "Medical travel insurance with a Big Tick Any condition. Any age. Any Destination." and "AllClear is the specialist medical travel insurance provider for travellers who have difficulty getting cover elsewhere".
Travel. SE is not here to give specific recommendations and I do not endorse any of the above (nor have I any connections with any except that I myself am covered by one of the companies mentioned by Which?). However it does seem possible to obtain the coverage you seek. A good price would require shopping around, which we are not here to do for you.