I think that is what most people who have done conversions say, and I would also be inclined to believe Frank de Haas when he says shorter cartridges can give trouble too. It is hard to judge from the rifle, but I believe mine, although dated 1926, has the original length.
I don't believe the Greek rifles made by Steyr were inferior to commercial versions. Numrich Gunparts do have some spares, although not the magazine spool:
https://www.gunpartscorp.com/gun-man...uer/1903-greek
I wouldn't try to convert a 6.5x54 into anything, as the advantages would be extremely slight. But since you are equipped for it, the .22/6.5x54 should be a good one. For those who aren't, the .220 Swift bears thinking about, although I wouldn't load it the way some people do. The biggest trouble you are likely to run into would be deepening the extractor groove and making it a true rimless instead of semi-rimless. But you might even get away without that. It has a slightly narrower shoulder than the 6.5, a little further forward, but that seems an easier alteration to the spool, with less of an "Oops!" factor, than a larger case diameter.
If I felt brave enough to lathe-turn a complete new spool (for which Numrich do have the bearings and spring which do the rotating), I believe I would start oversize, cut complete chambers, and then turn it down until I reached five lots of fresh air. But I wouldn't try... No, I've already said that.