IDEAL | Rubik's Blocks Cube: Twist, Turn, Learn | Brainteaser Puzzles | Ages 8+
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If you're manoeuvres to swap two corners and twist three corners on your final layer do flip edges, you could use these and their reflections instead: Swap 2 corners: R U' L' U R' U' L
Rubiks Blocks - Etsy UK Rubiks Blocks - Etsy UK
I would suggest starting to look ahead (which you might do earlier than this, but could do here), you know you will want all the top (as you show) edges to have the correct flip, this would be an ideal point at which to start combining your efforts - your method most likely does the corners next, but it is most likely that the manoeuvres you already use do not flip the edges*.