On the M39 stocks, I've found shims in the bottom of the receiver lug hole, tombstone shaped shims with a bolthole in them at the receiver tang, AND smaller square shims WITHOUT bolt holes in them placed at the backside of the cutout where the receiver lug rests. The shims that go in the bottom of the lug hole give the barrel it's float and work together with the shims on the receiver tang cutout to keep the barreled action from rocking in the stock and to allow it to fit evenly all the way from the lug to the tang.
The shims without the bolt holes in them are placed in the lug hole,standing up usually at the rear to keep the receiver from moving back and forth due to loose fit of the wood. When the receiver has excess movement back and forth under recoil it slams into the rear of the stock cutout and can cause the splits in the wood just behind the receiver tang you see on a lot of M39 stocks. You basically have 3 different adjustments going on with the use of shims. Barrel float,elimination of the rocking motion, and back and forth movement.If you sit your stock in a clamp type rest and place the receiver in it without the two bolts, you can tell if it fits flush all the way thru or has a rocking movement.Since barrel float is acheived with the front bottom shim in the lug cutout, you'll have to adjust that into the
rocking movement emlination at the sametime. The shimming to eliminate back and forth movement is a separete adjustment and shouldn't be effected by the other adjustments.
Your target rifle stock still has the same receiver placed in it and the same cutouts in the wood, so I would think the same would apply there, although I havn't seen one yet.I would think that if you made sure the lug was back against the back of the lug cutout hole in the stock and the two mount bolts were tight that you wouldn't get any recoil damage but the Finns placed them there in a lot of stocks and I have seen several stocks with splits just behind the tang.You could bed the action into the stock channel and probably eliminate all of the shims except for the shims in the bottom of the lug cutout but that's a different topic and I prefer the shims myself. I hope that helped and if someone else has a better explanation, please feel free to chime in. I don't claim to be any kind of expert on this topic, it's just my expereince on the 13 M39 rifles I've owned. Also, when you have your barreled action laying loosely in the stock, back and forth movement is easy to detect then.