Adjust a Shimano 105 9x rear derailleur
I think the problem with your procedure is that you are adjusting the limits but not adjusting the indexing explicitly. Try working through the detailed procedure that Park Tool recommends. There is both a video and written instructions on this page.

Check your derailleur hanger is straight. A special tool is required to do this accurately, but you can eyeball it by picking up the back of the bike and looking down the chain. The derailleur cage should look like it is parallel with the chain rings.

Another possibility is that your derailleur is getting worn and has developed some slop. There may be play in the parallelogram pivots, or the top jockey wheel has excessive play (although note that top jockey wheels normally have a few mm of lateral movement).