If the thickness of the butt extension was at least 3/4" I would use biscuits, they are a football shaped hard wood connector that once glue is put to it swells and makes an unbelievable strong joint. If you know any wood workers, they ahould have one. The biscuits come in #20, #10, #0, and FF. Sizes range from 2 1/2" -1 1/8" long. A #10 or "0 would be right for this.
Actually with todays glues, how strong they are, you really don't need any mechanical fasterners. I've glued wood alone and broke it and it has never broken on the glue line. End grain will suck up more glue and is easily broken with the grain, but that is not the case here.
Most important thing is your cut, a sled is fine on a table saw so long as it is held down firmly and that you have the stock orientated to the blade and use at least a 60-80 tooth carbide blade and tape the area you are cutting. On a radial saw tape it also and now you will have to build a hold down to secure stock.
The cutting depth on a 80 tooth is I believe 1 1/2" in depth so you might be alright.
Good luck and let us know how you make out.
