Those numbers look right to me, that is probably the easiest , most accurate way to go, but maybe mot the cheapest. Another way to do it is use brad point drill bits ,drill your 7/8 hole to proper depth , change to 3/4 bit drill your next step and then finish with a 5/8 . The brad point leaves a small hole to help center the next bit. Forstner bits with the brad point on them will work the same way. This isn't rocket science , it only has to be pretty close, it is all going to be on the inside where it doesn't show anyway. That is how I do mine, but I don't do very many, if I did I would go with the pilot point counter bores.
Wes