Ryan,
I had to upgrade as well or dealing with that process just recently. The steps you listed above are the Cisco recommended steps but for some reason it didn't work for me.
We upgraded from 5.3.x to 6.2.x. promote / démodé one CM from Prim to Stand also didn't work. configuration wise it worked but we wasn't able to verify the validity of the DB.
We had to rush all the upgrade and we took longer downtown to get everything going at once.
Primary upgrade from 5.3.x > 5.5.x > 6.2.x this was the mandatory path of upgrade.
we done both at the same time. no general outage caused by that. meaning all the field WAE was doing fine for them self with out CM for about an hour.
End result success.
Note we have to back up the database manually since we had trouble to pass it alone to the standby at that time and than pool it back as Cisco docs suggest. it just didn't work for us for some reason.
Best,