You don't need to go through all that.
Just catch all the fish and transfer them into a bucket (make sure you cover it so you don't get any suicides while you're at it). The darkness will keep them calm while you do all the work. If you have a bubblestone, put it in the bucket as well to provide extra oxygen. If you don't have one, just check the fish from time to time to make sure none are gasping for air and work relatively quickly so they don't need to be in the bucket too long. Alternatively, if you don't have a big enough bucket, bag the fish an let them float in the old tank.
Now transfer the majority of the gravel and any filters from the old tank to the new. If it isn't already filled up with fresh, de-chlorinated tap water, do that now. Just a note here - if you add the filter and gravel to the tank and THEN fill it up with water, make sure you de-chlorinate the water BEFORE you put it in the tank - otherwise the chlorine will kill all the good bacteria in your filter and gravel which elliminates the purpose of using them
.
Don't use any of the old water in the new tank. It doesn't contain anything useful.
Then turn on all the equipment - lights, filter etc. Just make sure everything's working ok and then start adding the fish from the bucket. If you have been keeeping up with water changes in the old tank, there should be no noticeable difference in water chemistry so the fish will be fine as far as this goes so acclimatizing each one isn't necessary.
The reason you don't need to wait to add all the fish at once is that the old filter and gravel contain all the bacteria necessary to support the fish that you are transfering. If you let the tank run without fish (and therefore without a source of ammonia) for more than 2-4 hours, the good bacteria starve and start dying. That can only lead to ammonia or nitrIte spikes so is not good for the fish.
If the new tank also has its own filter, run this along with the old. After about 2-3 weeks, you can remove the old filter as enough bacteria should have colonised the new. Alternatively, rather than moving the whole old filter to the new tank and running it alongside the new tank's filter, just transfer the old filter's media to the new filter.
Also, if you want to use a different gravel in the new tank, put the gravel from the old tank into a ceramic bowl or a (new) stocking and place it in the tank so that it doesn't mix with your new substrate. After a month or so you can remove the old gravel bit by bit - but don't remove it all at once.