Instead of using the steel punch as a glue block, try turning a piece of scrap maple or other close-grained hardwood as a dowel, and use it as a glue block instead - I've had good luck with CA using wood glue blocks - just make sure you give it enough cure time.
I usually put medium or thick CA on the small piece I want to hold, and spritz the face of the glue block with accelerator, then attached the piece to the glue block, hold for a few seconds, and spritz any glue squeeze out with accelerator.
Make sure the face of your glue block is trued up - no high or low spots.
Also, to help center your "button" on the waste wood, I usully draw a series of concentric circles on the face after I true is up. You can also bring your tailstock center up to the other end of the button and use it to "clamp" your button to the glue block while you wait for the CA to cure.
Another option is to make a dedicated glue block that fits directly into your headstock spindle, instead of using a collet chuck to hold a dowel. Check out this link:
http://www.woodturner.org/community/youth/projects/MorseTaper_1.pdf or here:
http://www.syzygywoodworks.com/news/2010/08/30/turning-a-morse-taper/