The way I do repasting is similar to what you described up until the cleaning portion.
From there, I use electrical tape all around the CPU and dGPU silicon die as close as I can. I then create a flat layer of paste that covers the entire die evenly. After that, I remove the tape, which leaves a perfect flat two-millimeter layer of paste perfectly on the die.
The next step is critical, which is mounting back. Do not just tighten it down based on number order. Place the entire mount gently in its place, using its screws as guides. I like to go over each screw and turn it counterclockwise until I hear it pop on top of its screw slot. I do that for all screws to ensure that they all start in the same position. Then, go by the numbers, tightening them back, but only do a 1/4 turn at a time, going around until they are all tight. This ensures that the plates are not deflecting the paste to one side or the other as it's being seated back.