I'm not an expert when it comes to the Model 10, so hopefully someone more familiar with it will chime in. However, what does seem interesting off the top is that it doesn't have a decimal tabulator, the front cover is flat - not bevelled, and the line space lever seems more robust than the one on my 1914 Model 10. All of this, along with the 60,000+ serial number, has me leaning toward it being a ca. 1926 production model.

If you're going by the information in the Typewriter Database, then you're right; the L-series was apparently discontinued in 1925. However, the Database is not an absolute. Its information has been pulled together by the typewriter community and there are often inconsistencies and missing data. Some even claim that the manufacturers themselves kept sloppy records. However, we can't ignore that your machine has a number in the 60,000 range, and for me that's something I put more stock in than the prefix information. With Remington portables a two-letter prefix indicated the model (first letter) and the month of manufacture (second letter). If your 10 follows this practice, the P would indicate that it was made in January.

There are numerous reasons why there might be an overlap in years, prefixes, and numbers, and the fact that your typewriter was likely a special order - and for export no less - is just one reason why it doesn't neatly follow the serial number rules. 

As for the S-variant versus the regular 10, as I previously indicated your machine doesn't have a decimal tabulator, nor does it appear to have the single-key tabulator that appeared on the Model 12 around that time, so perhaps it just indicates that it's a more base model? 

If I come across anything more concrete I'll be sure to post it here.

I can't give you a definitive answer since it probably would have depended on how many Cyrillic keyboards Remington was selling at the time. The type slugs may have been outsourced, so it might have been easier for Remington to keep a small stock - either of the special slugs or completed machines. Then again, there might have been other ordering options such as a Cyrillic keyboard with a choice of specific characters. In that case it would make more sense that they were made to order.

I would never describe it as rare (it's a very overused term in typewriter circles). Is it less common than a Remington 10 with a QWERTY keyboard? Absolutely, but I'm sure there are still plenty of Cyrillic models kicking around - enough at least that they wouldn't be considered rare. Value, when it comes to typewriters, is dependent on the buyer. I wouldn't pay a penny more for a Cyrillic keyboard, mostly because I don't have use for one, and if two Remington 10s were sitting side-by-side, identically priced, one with a Cyrillic keyboard and the other with a QWERTY, I would buy the QWERTY machine.

Of course there are a few collectors - not many that I've come across - who collect keyboards and typefaces, and it's possible that such a person might pay more for such a machine. My point is that you're not sitting on a gold mine, and what's it truly worth is what you'd be willing to pay for it, or sell it for.