Keep as much of the old water as possible, in buckets only used for aquarium usage. Put your fish in these buckets too.
Use water from the tank to keep the old gravel wet. put in the new gravel, and do the stocking idea with some of your old gravel. Add back the old water, same as you would when setting up a new tank.
What kind of filter do you have? Do NOT change the filter medium when changing out the gravel. put the filter media in one of the buckets with the old water, that way the good bacteria on your filter will still be alive. Between that, and putting back some of the old gravel in a stocking like you said, you should be good. Test your water as if you had set up a new tank. you shouldn't go through an entire cycle, but you should test to make sure levels dont get out of hand. For the first 2 weeks, feed every other day, let the bacteria get established.