Would it be possible to skim through it cheaply considering I already have the hours, or would I have to obtain all FAA approved course training hours?
No, I don't think you have to do the "approved course" (FAR Part 141 regulations) for your PPL, you can go the much less stringent Part 61 route. You could still attend the ground school (six weeks) but there's no need to burn money - for example on cross-country flights - you would just do lessons on a "as needed" basis. You fly until you are up to speed and got the minimum requirements down - here are the regs:
Electronic Code of Federal Regulations:
The IFR course is also a Part 141 course, so should there be any restrictions for your visa (I assume J-1?!) that the training has to be "structured" (?), this course would meet the requirements.