Suppose:

I take the minimum required of troop type X.

The army list allows me to regrade some X to Y.

If I regrade some, have I still met the minimum requirements for X?

Example: 3534 Khazar

"Royal Army Horse Archers" have a minimum of 8

"Regrade Royal Army troops fighting like Muslims" has a max of 8.

So would it be legal to take 0 "horse archers" and 8 "fighting like Muslims"?

Yup.