I currently have a Arisaka, MKIII Enfield and Mosin. Had a K31 I sold for $200 years ago.  I don't shoot any of them because of Ammo scarcity.

Is there anything out there in the venerable 7.62 Nato? I recall the French Mas was converted at one time. Frankly a 98K would be perfect, but I don't feel like sourcing 8mm.

54r ammo for your Mosin can be had for 40 cents if you look. Cheaper than buying 7.62x51. 2A1 Enfields are 7.62 and can be found for $450-550, FR8's for about $550-750. Chilean Mausers were converted to 7.62.

I have an Argentinian Mauser converted to 7.62x51 by their arsenal. It was purchased back in the nineties though.

Spanish FR-7 or FR-8. Israeli 7.62mm NATO Kar98k

Recently picked up an FR-8.  Neat rifle, not sure why I bought it, haven't been to the range yet.  The Israeli K98 conversions have gotten scarce in recent and in any event every one of those I've seen has been beat to within an inch of its life.  The Ishys of course, looked at several over the years.  Mostly rough but serviceable.  The Spanish converted their 1916 model to 308 but I don't know that I've ever seen one on this side of the pond (other than the FR7).

The MAS rifles I think have problems converted to 7.62.

I had one and it would blow primers out but I dont think that was the normal issue. Its been years

The bolt guns, the MAS 36, had to make a modification to the forearm.  It was just held on my friction and would creep forward.  The semi auto 49/56 was a different creature all together.  308 ammo operates at a much higher pressure than 7.5 French.  I never heard anything good about the conversions.  And all of these mods were made by Century.

The issue with the 49/56 Century conversion is that the bolt opens while the bullet is still in the barrel.  That causes a case bulge and sometimes the case swells in the chamber and the extractor tears off the cartridge rim ( yes, the extractor is that strong).  I curse Century every time I look at my 49/56 in the safe and can't use it.

The Chilean Mausers can be a good deal. The long rifles had a chamber insert that can fall out but, the 1912-61's used surplus NIW '03 barrels that were shortened at the back end to allow re-chambering to .308. I got one years ago that was cosmetically challenged but, had a nice bbl. When I got it out to the range, it had a broken firing pin and the chamber was too short to fully close the bolt. The shop that sold it to me was generous and credited me the cost of having the chamber reamed and a new FP towards my next purchase. After working out those kinks, it is a great shooter with what was an unfired bbl.

There are also Columbian and Belgian Mausers out there in 30-06. My Belgian 1952 it smooth and accurate.

As fas as oddballs that are easy to feed, there are some slightly sketchy Arisaka carbines out there that got rechambered into 7.62x39mm

I have a couple of Navy M1s in 7.62 NATO.

I prefer shooting them to the 30-06 ones.

There are some Israeli Kar98K conversions to 7.62 Nato.  

You can always buy a .30-06 Garand and convert it as well.  

But it's worth doing the math and finding the break-even point between buying a new gun vs buying ammo for the guns you already have.

03 or 03a3?

Argy Navy FN49s.

My 1912/61 had the same issue with the short chamber. Great shooter after getting the chamber reamed though. Apparently that isn't that uncommon on these.

I have a converted 1916(?) Spanish Mauser I bought a few years back for less than $200.
Pre FR- 7/8.
I think they mostly saw drill, training and guard duty use.

The K-31 could have been easily converted to 7.62x51.

Didn't notice it being mentioned before, but perhaps keep eyes out for an Ishapore built in 7.62?  Ive had great luck with mine,, they used to be a great value, but like anything else that's largely changed

Still, I have to wonder why you are worried about "sourcing" 8mm if you want a Mauser.  You're on the internet, last night I "sourced" a pair of flip flops from Amazon... That's about how easy ammo is.

$$$$$$$

There are three guns in my collection that are my absolute favorites and are the jewels of my collection. One is a 1972 S&W Model 15. This was just a lucky gunshow find. It's nothing rare or special but is in really nice condition and I just love shooting it. The second is a 1952 Argentine Sistema 1911 that I sent to John Harrison back in the early 2000's for a custom rebuild. It came to me with a cracked slide so the seller sold me another Sistema for half price, and then I sent the broken gun to John to have him fit a 70 series Colt slide and then do some custom work for accuracy and reliability (beavertail, improved safety lever, trigger job, new Kart barrel, open the ejection port, tune the ejector and extractor). That gun also handles and shoots beautifully. It's got a bit of an 80's vibe with a Tripp's hard chrome finish and Pachmayr grips, but it's still very much a 1911A1.

The third is a 1942 Springfield Garand that came back from Denmark and I got it through the CMP as a service grade. It had a lot of problems, doubling, terrible accuracy, etc. I sent it to Dean's Gun Restorations and had Dean do his magic to convert it to 308, give it a trigger job, install NM sights, refinish everything, replace all the springs, and restock it. I got a Turner 1907 sling to finish it out. This gun is a real joy to shoot. Very accurate now and loves milsurp Portugese and South African 7.62x51. I highly recommend a Garand 308/7.62x51 conversion.

Dean is gone now and John Harrison is apparently not taking on custom work any more. I feel very privileged to have wonderful examples of the stellar work from these master gunsmiths.

M1919

Steinel's has 6.5 and 7.7 Japanese ammo in stock.  Not cheap but if you don't reload at least there's an option.  Reloading is the best choice.

How much ammo are you planning to shoot that it makes it wise to purchase a $400+ rifle versus buying loaded ammo or components for what you already have?

Don't get me wrong: I love 7.62N.