Hi Steven, stock splitting is a quite common problem with Mannlicher-Schoenauer sporters. All the turnbolt Mannlichers from the M1892 on up to the M1910 share this tiny excuse for a recoil lug. They inherited this design fault from their granddaddy, the German M88 commission rifles. On the military M88 this lug abutted against a contoured steel crossbolt, while the military Mannlicher and Greek 03 M-Sch stocks had a small steel plate inletted into the stocks behind that "lug". Unfortunately, OEWG Steyr omitted this feature on the 03, 05, 08 and 10 sporters. Split stocks are especially common on the harder recoiling 9.5x57 aka .375 NE M1910s. With the .30-06 1924 model, known in the USA as the "Sequoia", they introduced a decent recoil lug like the one on the Mauser. But, from my experience with my own M1924, their stockers sometimes missed the purpose of this square protrusion.
The repairs you suggest are temporary at best. Even with the best of glues the stock will split again. If your glue is really good, stronger than the wood, it will some day simply split alongside the old crack. To really preserve such an old M-Sch rifle, more radical solutions are on order. I have encountered two 08s and my own 24 so far that were in nearly unused condition. Why? All three rifles apparently were bum shooters from the start, so they were relegated to a rear corner of the gunroom and rarely used. On close inspection I noticed the recoil lugs hanging out in the air, no contact with the stock. Recoil was taken up by the lower end of the rear magazine wall, as apparently on your rifle also. But the mag wall acts like a heavy leaf spring under recoil, shifting the action and barrel back and fore, until the wood splits. My tested solution to the problem: I cut out a recess behind the recoil lug to take a hidden crossbolt, FI a piece of a woodscrew. If the stock is already split behind the magazine. I install such hidden bolts there too. Then I glassbed everything. Now, slightly relieve the wood behind the magazine to avoid contact there. If done properly, nothing of this permanent repair is visible from the outside.
BTW, what is the state of your and John's plans for a roebuck hunt in Germany? Up until now, I had little luck myself this year.