Learn something new every day 🙂 the only stumbling block might be "Some consulates may require medical records to justify the need for treatment in Thailand. ", if the treatment is available elsewhere, such as the home country?
Medical extensions are for those who are unfit to travel, and are for a maximum of 90 days at a time. They are not a way to stay here long term. Maybe your best bet is the retirement extension.
They are continuing the same employment, so they should just ensure their payments continue. If they take a lump sum, they would have to start all over again.
To be belt and braces, get a letter from your employer stating your last day of employment as ... Oct , then cancel your work permit, then go and cancel your extension, this can be done in advance,
OK you are on an extension and not a visa. There is no short term extension. If you want to apply in London for a new Non-B then you need to cancel this extension and your work permit, and have all the paperwork including a WP3 from your employer. I really don't think you have any options really, (let's hope I am wrong).