M85, if you have already finished a JAA ATPL course, you have already done 95% or so of the ICAO Flight Ops licence course and you'll have no trouble working through the FAA ticket technical content, just the FAR's, AIM and US Weather to study. I suggest you don't waste your time on the AVTECH course. If you are after a dispatch qualification then you should do the FAA licence or find a country that will give you the ICAO FOO ticket based on your JAA licence. You might consider The Glasgow School of Nautical Studies, they have recently re-issued their ICAO Flight Ops Officers course- see their website.
But your JAA ATPL studies already give you all the technical content you will ever need for airline ops, you'll just have to get to grips with operational control, crewing and comms. With a JAA ATPL course completed I'd say you're already in a good postion to get hired into an airline ops department. Question will be however, why aren't you flying???