About the only thing I have to offer is my opinion, as I don't have a M77I (yet!).
I've admired those long stocked rifles for the longest time. Probably since the first time I ever hefted a MS with a spoon handle back in 1978. The rifle had this worn look that spoke not of abuse, but use. As I recall, it had a wonderful balance, and it just flew to my young shoulder. Chambered in something I wasn't familar with at the time (6.5 MS). It's price tag was too hefty for a young teenager, so she ended up being sold to a flatlander...
Anyway, I like the idea of the Mannlicher style stock. I realize that having that much wood along the whole length of the barrel introduces all sorts of accuracy robbing potential to the package, but I am willing to ignore that for esthetic reasons. Also, because of the distinctive 'European' look of that type of rifle, I believe that they should chambered for a suitably distinctive round. My first vote goes for a 7x57 Mauser. The 250 Savage is an excellent round (deer just love it!) and the 6.5 Swede would be another. If I were to get a bit crazy, then maybe one of the 9.3 caliber rounds after that.
Anyway, I have the feeling that today's emphasis on tack driving accuracy with any firearm that's produced doesn't hold with the mentality that produced rifles such as the MS. I think those rifles were accurate 'enough' for their purposes, and the stocks purpose (after all) was to protect the barrel.
So, my vote goes for a M77I in 7x57. I'd glass bed the action, check the barrel channel for any places where the barrel contacted the stock and correct them (if needed) and then I'd be happy as a clam.