Keith O - geez, that's great!!! No question with 10 head bolts you've got a 16hp in there. From the appearance of the head it looks original to me, as tho it's been untouched. The Serial no. should have 7 digits, and assuming it does since it starts with 81 that would indicate the engine was manufactured in early 1977 (Kohler manual shows serial numbers starting 80-89 as being in 1977 so 81 should be early). That time frame matches the build of your tractor, if I recall the other numbers. So, where does that leave us? I'd still like to see a clear pic of your tractor serial/build tag (the other was blurry). Someone could have certainly dropped a 16hp into a 1250 with hydraulic lift and lights, but for it to be a correct date code engine to match the tractor would be really unusual.
Hey, did you happen to count the cylinder cooling fins??? If it's 13 you have something special!!!!
(under edit) - in your pic of the Kohler serial tag it looks like your engine is really really close to the frame. Might be optical illusion. Suggest you try to pull your engine side to side to see if you have worn out ISO-mounts. Also, you should have the Kohler tag on the side of the shrould below the serial tag, and below the timing site hole. You might need to push the engine towards the right side to see it.
Tom H - you drinking soda pop in the morning?