My main focus would be to preserve your existing filtration. You should be able to completely swap over to new substrate and not effect your nitrogen cycle at all, provided you used the same established/seeded filters on the new setup. I've switched over to complete new setups, just using the old filtration and had no cycle issues what so ever.
Like said, fill a storage tote with dechlorinated waster of similar temperature and transfer your filters over to this. Net out your fish, get them into their temporary home, empty the tank as far as you can and shop-vac out all the old substrate. It's so easy this way, but you have to empty the shop vac often or it will be too heavy. Wipe/scrub out the tank with tap water and shop-vac out the crud if needed. Add your new substrate, refill with new dechlorinated water of similar temperature. Get the filters running on the tank, add your fish. Done! Like said, I've done this several times. No issues. Pretty easy.