I've made quite a few myself with good success rates - I personally like to use the credit-card sized diamond plates and wet sand them and I work from both sides once the inital hole is made. If you have a larger needle on hand, once the hole to size insert the point as far as it will go and gently turn it without enough effort to expand the hole further. It will burnish any jagged edges that might exist and help true up the circularity as well. Do it from both sides as a final measure and you are good to go.

PS these are the plates I talk about (amazon should have them but they are not hard to find in any case) -the 600 grit works just fine but you may want to use the 1200 to finish but it takes forever to do it all with that one: