Yes you are correct .... 12v - 24 v Not a problem ..
So yes you are right , but speed must be "LIMITED" to 15mph, IF its capable of more than this then thats where the problem is, also weight limit etc.
Once mods are done and equipment changed, you are moving towards the Classification changing from Electrically assisted tricycle to Motor vehicle and the law relating to construction and use regs etc.
But as i said, a bit of common sense and being sensible by not doing anything thats going to attract attention and every one should be ok.
There wont be any Traffic officers left soon anyway so won't be a problem