Excessive headspace is not uncommon on Mannlichers and Mannlicher Schoenauers, I have a number of them and all bar one has excessive head space, 0.018" in several cases. This is often accompanied by cratering on the bolt face around the primer pocket.
If you are a hand loader then you can correct the problem to a degree by resizing the brass as described above. If however you are not a hand loader and want to use old or new factory ammo then you will need to correct the rifle.

First however you need to find out whether or not you have excessive headspace. Go-No Go Gauges only work if you are within headspace but if you have excessive headspace they will not tell you by how much. The easiest way to do this is with clear packing tape which happens to be 0.002" thick and compressed (at least in Australia). Cut a small square slightly bigger than the case head size and then firmly press it onto the case head of the ammunition that you intend to use. Then take a box cutter with a brand new blade and trim off the excess packing tape. Place the cartridge in the chamber and close the bolt. If the bolt closes easily cut another square and press it on top of the first one and again chamber the round and close the bolt. Keep doing this until you can just close the bolt firmly. Measure the stack height of the tape and subtract 0.001" and you will have your head space measurement. This method is easy and very accurate as the tape will not compress any more and you get an accurate reading.

You then need to work out where the excess headspace is, ie. in the chamber or on the bolt head or both. To check the clearance between the bolt face and the barrel face you need to remove the extractor and the ejector from the bolt head and remove the firing pin. Cover the bolt face with a layer of packing tape and trim. close the bolt on an empty chamber and continue placing layers of packing tape on the bolt face until the bolt is hard to close. Measure that and this will give you the clearance between the bolt head and barrel face. Subtract this amount from the first measurement and this will give you the amount of headspace in the chamber.

However before you go and correct the headspace you need to see whether or not the barrel shoots. You can do this easily by using some factory ammo or hand loads. You will need to build up a disc on the rear of the cartridge equivalent to the original headspace measurement minus 0.004" to give you a desirable amount of headspace and allow the bolt to close properly. Then cut a cross through the tape where the primer is to allow the firing pin to penetrate without resistance. Do this for ten rounds and go and shoot the rifle to see whether or not the barrel is any good. This way you can check the rifle for accuracy without having to alter the brass and you won't get head separations and split cases. All my rifles have oversized grooves but shoot normal 0.264" bullets accurately but if not than you can try some 0.267" bullets and see what happens, but only if you have oversized grooves which you will have to measure to determine.

If the rifle shoots like a dog and you are sure that it is the barrel than you can re-barrel the rifle and correct the headspace with the new barrel. If however the rifle shoots really well and has special interesting proof marks which you want to keep than You will need to correct the bolt face and on a Mannlicher with rimmed rounds you can also correct the barrel if it has excess headspace there. This can be done by laser welding the shoulder for the rim and then setting it up in the lathe and turn a new shoulder. The bolt head can also be laser welded and than ground to the correct thickness but you will need to make an accurate jig to hold the bolt head while machining. You can also have the bolt face hard chromed and then ground to size but this will not take any blueing so if you want a blued bolt face than you will need to laser weld. If the bolt face is cratered than this can be fixed with laser welding at the same time. In all cases you will need a jig. You will need to measure the firing pin hole run out as well as firing pin hole size with pin gauges. These can be a bit of an odd size and as you will need to machine the hole after welding to remove the weld that has filled the edge of the hole, the easiest way is to set the jig up in a rotary table and clock up the firing pin hole and than use a carbide and mill that is smaller than the hole and machine it out until you just touch the original bore.

I realise this might sound a little tricky and requires a lot of machinery but it is the only way that I have found to fix the problem if you want to keep the original barrel and sights etc.
Depending on how much you have to build up the head you may need to also check firing pin protrusion and correct if necessary.

I have found that once the headspace is corrected even Kynoch brass shoots without any stretching of the brass. I was lucky enough to pick up 11 boxes of original Kynock 6.5x53R factory ammo and did the above test with the tape and fired the ammo, checking for any stretching and there was none. I then cut a case in half length ways and measured the wall thickness and there was no thinning even though the brass was 0.010" thinner than my Winchester brass for my 338 Win Mag.
I believe a lot of the negative press that Kynoch ammo got for splitting and head separation was because of excessive headspace which the owner of the rifle had no idea was present. I bet that there are a lot of old sporters out there with excessive headspace but the owners don't realise it.

Hope this helps.