Kitz is right....if the part is relatively easy to carry, take it to a
machine shop that burns out taps...they do it regularly. It may
not affect the threads but you can always install a helicoil.

Also, most ez-outs are not carbide....a carbide piece would be
pretty expensive......usually they are just harder than heck.
You might try a real carbide drill if you can get it started. A real
carbide drill (not a carbide coated cheapo) is available from the
big supply houses. You'll have to have a good flat starting spot and
you will probably not be able to center punch the starting location.