I do not know what the Schoyen stock looks like so I cannot comment too much but be prepared to wrestle with two things.

1.  Schuetzen stocks have enormous drop at the toe which gives fits when shooting off the bench.  A butt-sled is a useful idea and one that I'm pursuing now.   

2.  Think about your trigger.  Very carefully.   

I've made (making) a Zischang Borchardt and these issues are not trivial.  It can be done, but there are many easier ways to go.  I'm not there yet, but I'm getting closer. 

Brent

A butt sled is simply a flat-bottomed wedge that is grooved on is upper angle to fit the stock and give it a wider flatter base to rest on when shooting off a bench rest.
The groove in the wedge is fitted to the contour of the bottom of the stock.  Typically they are pretty well hogged out with a router or mill of some sort and then the stock is waxed and wrapped in a layer or two of saran wrap and then the groove is coated liberally with acra-gel, the rifle butt clamped tightly into the gel-filled groove and allowed to set up.  When cured and removed it should be a good tight fit to the stock.  The flat bottom of the wedge is is laid out so that when the rifle is in the wedge groove, the bore line will be parallel to the bottom.  Or, when the gun is in a rest and in the wedge, with the bottom of the wedge on the shooting bench, the bore will be level. 
  The width of the bottom or foot of the wedge has to meet whaterver your rules permit for benchrest stocks.  Length may also be goverened.  The whole affair should be tall enough to let you work the action and have the bore level without being too tall and tippy.  S
ome folks attach the wedge (or butt sled) with a screw or bolt others use double stick tape.  I imagine, rules permitting the butt sled could also be weighted

I gotta disagree with that mg.  What does "shoot well" mean.  I'll put my offhand optimized .22 up against any bench rifle.  It consistently shoots in the 240s at 200 yds off the bench, and yet it is built specifically for offhand with a hooked plate, an inch of cast off and a back bored tube.  I don't think that winning rifles have to exclusive to just offhand or just bench. In fact, I've been beaten too many times and I have won too many times by "all round" rifles to believe that.  

I just built a butt sled for my Zischang Borchardt.38  today.  If it works as well as I hope I fully believe I will clean house with the rifle off the bench or offhand.  

I would argue that switching out stocks just gives you loose wood/metal fit and eventually poorer scores for your trouble.  I would not argue that really hard, but I'm not afraid of a bench rest specialist rifle.  

Brent

My humble opinion is that if your rifle relies upon wood screws for its buttstock attachment, then you have my deepest sympathy (& pity).
Sorry, JMO, gooc luck, Joe

Adding a drawbolt is relatively easy, so I really don't quite understand the craftsmen who're still using wood screws. On Stevens and rollers, to name two.

Except that it's quick and cheap, for those who value that sort of thing.
Good luck, Joe

Plum,
another thing you have to consider for shooting a gun like that off the bench is that you will need a much elevated front rest.  The drop of the stock makes it darn hard to get the barrerl th point high enough for 200 yds, unless your range is shooting down a steep hill.   

I just built an elevator block for my front rest and the varnish is drying on the butt sled.  I hope to shoot it this weekend, but it will take a bit of luck to make that happen.

Brent