A while ago, there were a couple of threads (and a big debate) about amsoil and extended drain intervals. A couple of guys running it had their oil gum up, and I think it trashed some pushrods or something, and caused a cascade of valvetrain damage. Ford even denied warranty coverage saying the oil was not approved.
Amsoil (and rotella syn) may be great oils, but something is obviously causing them to gum up in a few rare situations. The idea of fuel in the oil (from the dpf regeneration cycle) was thought to be the cause. Extended drain intervals were also in question, but you're changing every 6k which seems fine.
You mention that water can be the cause of oil gumming up? I was not aware of that fact, but if true, and coolant made it into your oil, it seems like that could be a likely cause.
You mention that you've had 2 radiators replaced. How quickly was that issue caught each time? Did the coolant level ever drop? If so, check out the image below about cavitation and the mixing of oil and coolant. Going out on a limb here, but it may be related to your issue, and we may have another thing to watch, for those with failed radiators.
Credit to "BushPilot" on TDG.