Just read through, i didn't know there were new regulations on the insurance thing.
Anyway with 6 points i doubt it'll make much difference. On the form they'll ask if you have a clean license, it doesn't matter if you have 1 point or 12.
I think the nature of the endorsements however do matter, for example i doubt an airline will employ someone convicted of dangerous driving or drink driving, that kind of thing.
Driving without insurance though you might be walking down a rocky road. It all depends on the form and whether they require you to disclose the full details. In my experience in employment they usually just ask if you have a full driving license as opposed to a clean one unless your applying for a driving job.
I haven't (yet) worked for an airline though so i can't really help there. I've found though FTO's running schemes often ask for and require a clean driving license, Multiflight (West Atlantic) springs to mind. If your paying your way through modular or something similar i don't think they care.