I tend to agree with most of what you say. The double feed were due to poor timing, both on K98's. Case slips out from under the extractor claw, as far as I could tell. Plenty of other problems with the 98's that are common with push feeds to. There big advantage is that massive extractor claw.
I bet it is not a "timing" problem. When you cycle the bolt back all the way as fast as you can, there is no "timing" involved, just practiced as fast as possible reloading. If timing is required to eject a case from the chamber there is something wrong with the gun.
I bet the tip of the extractor was damaged, this damage normally occurs when a round is placed on top of the stack in the magazine and the bolt then closed(as many people do when using a push feed. This forces the extractor claw to have to snap over the rim of the cartridge as the bolt is closed. It was never designed for this and is a big no no for Mauser type actions. You need to load it with rounds from the magazine only or ensure the extractor is over the rim before closing the bolt if carried one up and a full magazine.
The problem could also be that they used a K98 which was configured from one cartridge and then rebarreled to a different cartridge resulting in the extractor claw not fitting the new case. Incompetent gunsmiths don't look at this competent ones do. You wont find a Rigby or H&H if built on a K98 with this issue unless the extractor tip has been damaged.