One thing first. Since you mentioned that you are living in France right now, I suppose you have a work visa. The UK is a third country now. If you leave your job in France and move elsewhere you will not be coming back easily. The visa will be gone and you will not get a work visa as a helicopter pilot in the EU. They have enough. No mountain flying in the Alps for you. Even a digital nomad visa will not help you. If you keep your job and do a mondular course in France, you have a much bigger job market. Keep that in mind.
And don't blame the EU, that was the Brits decision. They knew the rules before they left, because they helped writing them.
I have heard good things about Hillsboro. That is really a good way, not the cheapest one, but Hillsboro has a good reputation in industry. If you can get an instructor job in the US, good for you. Always better to come home with a 1000 hours than 150.
EASA has a list of approved flight schools outside the EU and I can not find Hillsboro, therefore ask them who's licences you will get. They claim they are the only helicopter flight school with an F1 visa. Since Trump and Brexit, things got harder for training in the US.
You can always try to do something more complicated like Agile suggests, but things have probably changed quite a lot since he did his licences.