The easiest and fastest way possible to have a JAA certificate is to obtain a "temporary" one year certificate through a contract a company that hires you and sends you to formal school in the US that has an approved JAA training program. That training only lasts about a week.
A former colleague, already Lear 45 rated, did just that. He attended the school in Dallas, passed the check ride and was flown on British Airways to Europe. He worked six weeks on then six weeks off until the termination of his contract.