It has been very difficult for the past several years for nurses to obtain work visa sponsorship and so far that hasn't changed. Before you can apply at a university to do the full-time Overseas Nursing Programme, you'll need a sponsored offer of employment or clinical placement which requires a work visa. Teaching nursing in the UK wouldn't be an option without NMC registration, which won't be granted until you've completed the Overseas Nurse Programme. As far as the demand for advanced practice nurses in the UK, as you said it's still fairly new and the job vacancies aren't plentiful. Realistically it's not something that would lead to work visa sponsorship.
The ONP is only 20 days long and there is no clinical placement needed if your original training was done in the old "commonwealth" countries as my professor said while I took it, i.e. USA, Canada, Australia, New Zealand, etc.
You also don't need sponsorship to do the ONP either; I did it as a regular visitor last year and all I had to show was my letter from the school to the border guard.
IELTS was pretty easy too...it might be helpful to look at the format, but I didn't really study.
You can check out the UK forum on allnurses.com for more info, there are a few people going through registration/gone through it.