I've tried a couple of things since I posted the question.
First, I threw in more wax to make the mix a little harder at room temperature.
Second, I took a 3/8" steel rod and made it into a mandrel by chucking it into a large drill press and by filing it it down to about .358" OD. I then took a spent 7.62X54R steel casing, drilled out the primer and opened up the hole to 3/8".
Next, I stood the case upright on its rim, lubed the mandrel and used the drill press to press it through the case opening, expanding the mouth and neck of the case to .358" in the process. I turned the case over with the stuck mandrel in the case and used a hammer and punch to drive the mandrel back out. I then cleaned up the inside of the case mouth with a reamer and filed the outside of the mouth to sharpen the case mouth to make slicing through the wax easier. Sort of like a cigar punch.
Last, I bought a 3/8" wooden dowel and cut a piece with the same length as the 7.62X54R case and stuck it in the case to be used to push the bullet out of the case.
The homemade kutter works well at removing bullets from the wax but is a bit messy.