CIP gives 10,45mm for land and 10,75 mm for grooves with the 10,75x68,
but the only suviving rimmed 10,75 in the CIP list - the 10,75x49R Gründig have 10,20mm land and 10,75 mm groove so it was not completly unusual.

the rimmed cartridges and the rimless like the 10,75 x 57 and the 10,75x63 were all loaded with the same 350 grains bullet.
I would say the 10,2mm stamp on the barrel indicate that a gauge of 10,2 mm diameter pass the barrel in the proof house. so lands diameter actually could be more close to 10,30 mm.

the 10,75x57 was not a big success than but imho, it works by a combination of the little shoulder and the case mouth. I have such a rifle,dont make thousends of shoots because lack of time in general but had never an issue when firing it.
the shoulder is there and more to feel with the finger tips than to see with the eyes.I dont have much more informations about the 10,75x61 Haenel other than it exits but will ask friends who have maybe some stuff. would be good to see the factory ballistic to know what to load for.
I believe it came later than the other 10,75 mm cartridges and was offered only by C.G.Haenel in Suhl probably in Haenel made Mauser 98 hunting rifles, the Haenel M 1900 and 1909 also the older M 88 hunting rifle.
In Suhl there were a lots of firms side by side, all were knowing each other if not being related.
When Kettner get an order for a Mauser in 10,75x61 the rifle was build in the Kettner shop geting the barrel from the same barrel maker like any other, small parts were taken from a special maker who deliever any other gunmaker in Suhl with the same parts, if they dont had an engraver in the house the rifle was send to an engraver in the next street who made the same standard engraving on the rifle he did for all other firms.
in the end someone walking to the haenel factory and borrow the rare 10,75x61 chamber reamer for Kettner and your rifle and bring it back when the chamber was done.

if it was my rifle I would send the chamber cast to ch4d for a die set, had only the best experience with them. could be you are better with hawk bullets than woodleigh because they are softer.
the muzzle velocity was maybe +/- 620 m/sec with the 350 grains bullet, same like DWM was loading as special euro load for the 10,75x68.

to bad it lost the scope. my gunmaker would set another scope into the claw mount for 200 euro.