I hate having to recommend this chinese stufff, but you want cheap so here it is; use your regular 13/16 drill bit to go as deep as you can with it, then without moving anything use a chinese end mill (with center cutter) and plunge it into the hole to clear up the angle the drill bit left. These cheap end mills are...cheap, and you can get em from ebay, msc etc.
I wouldn't grind a drill bit if you are not experienced with it, if done wrong it will chatter like mad and might even twist and brake in the hole.
0.02 cents
H3ndriX