Old screws splitting at the screw slot are not that uncommon. I've had it happen a couple times, and seen guns with half a head occasionally. Glad it came out though, as they can be tough to remove.
Not many marks on Winchester rifles normally, and beyond the serial number on the left lower tang, other numbers usually wont correlate or match the serial number. Work order numbers are usually marked on the left upper tang, but not often on wood, or other places. But there are exceptions to the "norm" on many early guns.

Update:  I tightened everything up and the buttstock is actually tight to the receiver.  Then I went shooting.  It took me a long time to find paper but about 5 shots after I did the cam broke off of the firing pin.  I still don't know how this gun shoots but I do know what I am going to do with it now.

This gun letters as a standard low wall from 1888 in 22 short.  No swiss buttplate, no nickel.  Those were added later, maybe the factory or maybe a semi-custom, 'bitsa' gun.  Either way, nothing about this gun is original so I have no problem breaking it up for parts.  The action will be used to build a custom .22 silhouette rifle (Steve Durren may be getting a call soon), and the forearm, barrel, buttstock, and buttplate will be getting sold.   

Now that I know what I am starting with I get to envision what rifle I will get built.  It is great fun contemplating the possibilities...

Enabling is good!

And you are correct, that is not a standard 1885 swiss buttplate.  It is the swiss buttplate that Winchester used for the first 3 years or so of manufacturing.  It is exactly the same buttplate as was used on ballards and farrows.  

I would love to build a gun around that buttplate.  It is rare and beautiful and would make a great  piece to build a gun around.  The problem is just as you described; my silhouette match won't allow a swiss buttplate so I would have no place to use the rifle.  My current thoughts are:

#2 round barrel, 26-28 inches
No sights, MVA B5 scope.
Straight grip, semi-fancy/fancy wood with crescent buttplate.  
Set trigger

I do not own a scoped rifle so it would be a silhouette/benchrest/all around scoped .22.  I have never had anything custom made before and I have yet to talk to a gunsmith so all of this may be out of my price range but I like to think about it anyway. 

The buttplate does indeed look like the Farrow style used on Marlin Ballard and also Remington schuetzen models. My Ballards and my Hepburn Match B both have what appears to be the same buttplate.