Having explained your circumstances I can understand why you need a full throttle. Bearing in mind the highlighted part of your post, a full throttle used for any great distance will use up the battery pretty quickly. I only use it to move off sometimes or if I'm in the wrong gear. I've only used it for about 100 yards max. I can get about 40+ miles from the Yose 13Ah battery but mostly pedalling in PAS 2 (out of 5).
It's stretching your budget, but I think you should be talking to Woosh or Wisper about this.
Wisper can supply a certified UK legal full throttle bike:-
Wisper Full Throttle eBikes | Wisper Electric Bicycles (wisperbikes.com)
At 71, I'm looking ahead to what I might need in about 5 years time (assuming I'm still on the planet) and I'll be looking for a full throttle, step-through framed bike with a high capacity battery. Wisper could meet that criterea now.