Never heard of the 6mm Ryne. I would bet many gunsmiths used a pet name for their wildcat that we are not aware of.
PO Ackley's two volume book set mentions two cartridges that are similar. The 244 H and H made on a full length 375 H and H case maintaining the tapered case shape. PO said that it would shoot a 100 gr bullet at 3500 fps with 68 grs of 50 cal machine gun powder. I have no idea what powder that might be....He went on to say "when the load was reduced by 10 grains the rifle completely disintegrated." !!!
The other was the 6mm Atlas made by necking down a 264 win mag. At the time of PO's writings there were few slow powders. He said it was badly overbore capacity case which has to be loaded with extremely slow burning powders to get a degree of efficiency. He went on to say that good accuracy could be obtained with 90- 105 gr bullets. He said the gun got 3760 fps with H570 and a 100 gr bullet.
There is a version of the 6mm/7 Rem mag that Ross Seyfried put together. He necked down a 264 Win mag to 6mm. The cartridge is the same as the 7 rem mag just different neck diameter.
Ross ruined his first barrel due to as he put it: "a hard ceramic like coating in the throat" that he couldn't remove due to infrequent cleaning. He retired that barrel and was able to use the next barrel as he cleaned it often. He said it was the closest thing to a death ray he had ever shot. He used lighter bullets and vaporized a crow IIRC.
I cannot imagine the "fun" your friend had using it as a bench gun if it was for competition. With the fouling issue and short barrel life I would imagine it might set some long range BR records in windy conditions but he would have to own several barrels made up for a competition season.
Can you ask your friend about it?