Hey,
As my setup was VERY similar to yours (if you want to stick to not mentioning names, let's say it's the only EASA-approved school at Gillespie Field in El Cajon...), here's my feedback:
I did 4 exams in the UK before venturing out to the US and I couldn't get the others out of the way due to "rest of life" committments. It was a great help to get them done beforehand. Doing all of the theory exams while being in the US for 4-5 weeks is a lot. Really - it's a lot. You need to give yourself some rest, too, and it should be enjoyable.
I squeezed the remaining 3 (at the time) exams into the time spent in California and completed them there. I have to say, I scored much better grades on the ones completed calmly beforehand than on the ones I completed between actual flying lessons, even failing NAV on the first attempt.
US EASA flight schools are supervised directly by EASA so I don't think you can do some here & some in the US.
Interesting. When I was there in 2013, it was still supervised by UK CAA and I imagine it still must be? What state will issue the license upon completion? Surely not the US or EASA itself (they don't have the authority to do that,
AFAIK)?
I suggest to discuss this with the Head of Training of the flying school, too - he'll be on top of current regulations.
Good luck and have fun!