Cosmiccomet: I can identify with your position. The issue to HR or the outsourced company that processes applications does not understand the complexities of licensing, nor do they wish to understand. They are presented with boxes to check and it is black and white to them. In the old days, your CV would have bypassed HR and gone directly to the Chief Pilot, but that was years ago.
Your B744 is unfortunately on the wrong license. I know it is ridiculous, but this is how it is. Technically, you do not have a frozen ATPL, but simply a JAR Comm/ME/IR. Frozen ATPL would imply that you do not have the hours to get the ATPL and that is not the case. If you were to take the ATPL skills test in the B744 sim and then perform the required takeoff and landings in the actual aircraft....then you would have the B744 rating on the correct license (JAR license). Once you have the JAR ATPL then you will magically get your CV past the gate. I know what you are thinking, "if they hire me and then I go through their 744 training, then I can get the ATPL upon checkout. Ya, true, but that is not going to happen....in this market. You can't exactly rent a 744 to do your required take offs and landings either (after sim) to get the 744 on your ATPL license. That would be too expensive. The fact is that you need to get the ATPL. Don't worry now, that your 744 rating is not on that JAA license. Once you get the JAR ATPL, doors will open and ridiculous outsourced airline hiring firms will process your application. Right now, you are no better than the thousands in the pilot wannabe zombie army (in the eyes of airline HR).
Good luck.