Simple, compared with rimfire!
I apologize for responding in spite of never having converted a 7.62x54R into an 8x50R Mannlicher, but I have converted 8mm Lebel into 10.4x38 Swiss rimfire for my Peabody - and published photos to prove it. Compared with that conversion, the Mosin-to-Mannlicher is going to be a doddle!
All dimensions quoted are taken from the official German "Masstafeln" (Tables of Dimensions). Real rifles will differ slightly, so do not fret about tiny differences in nominal dimensions that you may find in other sources - in the end you have to deal with reality, and what follows is just a feasibility check.
The Mosin case is longer than the Mannlicher - good.
The Mosin neck has a wall thickness near enough the same as the Mannlicher - OK
The Mosin shoulder fits inside the envelope of the Mannlicher shoulder. Good
The Mosin base has a diameter that is noticeably less (12.37mm) than the Mannlicher (12.60) - bad, because on fire-forming the case will tend to bulge to one side. Works, but looks awful!
Do not despair - help is coming, because:
The Mosin rim has a diameter of 14.48mm, thickness 1.60. The Mannlicher case with a rim diameter 14.20, thickness 1.40. But this does not matter. Since we want to get a Mosin case into a Mannlicher chamber, what concerns us is the minimum chamber size for the rim recess. And this is 14.20x1.50.
It sounds as if this is not going to fit. But old rifles get looser, never tighter. Oh dear, I used the dangerous "never" word, time to backpedal and say "I have not yet come across a milsurp that has a chamber that was tighter than the specified minimum" so as not to provoke Murphy's Law!
Bearing this in mind, I suggest that you quite simply try to chamber a new, unfired Mosin case in the Mannlicher chamber. It will probably fit, since the shoulder will be within the Mannlicher profile, and the neck, although longer, should fit into the generously long throat of the Mannlicher. If not, you may need to reduce the rim diameter a touch. Maybe shorten the case to 50mm before trying again. I had the same consideration for my Peabody - according to the table of dimensions, the Lebel rim cannot fit. However, thanks to the apparent tendency of modern manufacturers to keep rim dimensions well below the specified maximum**, I discovered that 80% of the Lebels fitted quite snugly. The rest were only about 0.002" oversize, and just required a touch with a file on the case spinning in my lathe.
And this leads to a vital point. If you have a rim that fits snugly into the recess, then it will center the base of the cartridge and prevent the unsightly bulge to one side that would otherwise occur.
Now you know why I have written so much about the rim sizing. If you do have to reduce the rim, do it as little as possible, to maintain that snug, centering fit!
So the base end of the case will automatically be centered by the rim.
How about the head clearance? Note that I have not written headspace. Do not waste a penny on headspace gauges for such old rifles, despite what some armchair expert may tell you. Firstly, because it was a military rifle, and they tend to be generous in the chamber dimensions. Secondly, because it is worn, regardless of what it may have gauged when new, and thirdly, because SAAMI, for instance, was set up about 30 years after your rifle was manufactured, so the standards were derived retrospectively for civilian rifles. The gauges you can buy to evaluate modern civilian rifles are ACWOTAM as far as I am concerned for pre-WW1 non-US milsurps.
Back to head clearance. Forgetting all mumbo-jumbo, this is quite simply the amount of end-play of a real cartridge in that real rifle. I have described on more than one occasion how to measure this, so please be so good as to dig out previous contributions on this topic. For rimmed cartridges of that vintage it is quite simple - if you can close the bolt without force, then the head clearance is at least not negative, and it is worth measuring the actual value. Again, I prophesy that the Mosin rims are probably a bit thinner than the specified maximum, and the rifle will probably have a measurable head clearance with these cases.
All this was to check whether you can use the Mosin cases without major reworking. I suspect so.
Assuming that the Lebel cases can indeed be inserted into the chamber and the bolt closed without applying noticeable force, then all you need to do is:
1) Trim a few Mosin cases to 50 mm OAL.
2) Anneal the necks.
3) Expand the necks to the right diameter.
4) Load with a light first load, and fireform.
Since step 3) depends on the diameter of the bullet to be used, take the very first case and expand the mouth with a slight flare more and more until it rubs in the neck portion of the chamber, and shows a bright line when you remove it. Measure the diameter of the flared mouth and you have a figure for the absolute maximum diameter of bullet that you could seat and still be able to chamber the round with a safe clearance. Do not select the bullet just on the basis of wanting to fill a worn bore, or you may be creating rounds that are impossible or dangerous to chamber !!!!
I appreciate that all this may indeed appear to you like an armchair expert sounding off. Nevertheless, please try the steps I have recommended and post the results. At least, if I am completely wrong, my red face will not be visible!
**This is not sloppiness, but, since all production steps have their own tolerances, a precaution to ensure that the largest rim leaving the factory is within the specified maximum. With the result that the majority are measurable smaller!