Just a point on putting the IR on the converted FAA PPL. I was told that your FAA PPL is subject to the restrictions on the JAA PPL from which it is converted. The JAA PPL is limited to VFR flying so therefore your FAA PPL will always be based on that. Since (in the US at least) the IR is a rating on your licence and not a licence in itself, it will not technically overcome the restriction on your converted licence.
Point is, I ended up doing the FAA PPL flight test and exam so that my IR would be legit. The exam revision was worth doing anyway and the flight test was very relaxed. But it was an extra expense which I wasn't expecting and delayed my hour building trip by a week or so.
I know there are different views on whether this is correct - it might be worth checking with your school so there are no surprises.