The guide you a w referencing is for an M62, N62 is a slightly different procedure so I would advise looking up instructions for an N62

What you are describing is also not a full coolant flush. A full flush requires removing the block drains. Otherwise you will get out maybe half of the coolant volume. TIS has coolant volume listed in it, I am quite sure it's more than 2.2 gallons if you do a full proper flush.

Brass bleed screw is also imo a bad idea. The plastic bleed screws are rarely an issue, only a problem if you overtighten them. If you overtighten a brass bleed screw it strips the $80 expansion tank instead of the $6 plastic bleed screw.