Walking to the outside should not happen for properly adjusted top limit screw on derailleur. There are different things that can be done to improve shifting. Given the difficulty, I presume that are no ramps or pins there. The first is to try and rotate the outer ring on the crankset relative to the inner. The chain should have at least 2 positions where it can easily climb onto the outer ring, settling right away properly onto the teeth of the outer, while progressing from the teeth of the inner. Eventually around those positions you can work with the teeth profiling.