get a lot of buckets.
drain most of the water from the old tank into buckets, add fish. keep several buckets just for the water.
i would swish the remaining water and gravel around a bit and use a net to skim out a lot of the solid floating waste, then scoop the somewhat cleaned gravel into the water-only buckets. move old tank, put in new tank, put in rinsed new gravel if you need more, add gravel/water buckets and decorations, then start filling with dechlor water, run both filters when it gets high enough. when it looks settled, add fish and remaining water. do water tests and temp check beforehand.