I agree with rudestuff, do both!
There are a few ATO's in the USA that are approved for FAA and EASA training. A couple of them advertise that you can complete both licences for about the same price (no conversion needed) as just one elsewhere. Its all about how you structure it.
I suggest you give them all of them a call and talk through your options, but remember, run a mile from any ATO that's want you to pay more than 25% of the cost upfront. Keep you account no more exposed than that at any time - preferably less!
If you do your research properly you will be able to narrow down to a very short list those that will enroll you with just $1,000-$2,000 on account at any time - a safe place to be. Also I see one ATO urging students to just commit to the PPL and then decide afterwards taking it in stages to suit your budget and confidence in the market. I don't think anybody could go wrong with such a conservative and thoughtful approach.
Good luck....it might be interesting to others if you would post some details of the responses you get?