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These landing pages have been blocked for indexing through robot.txt (I hope this doesn't have any effect on QS)
It may be worth generating a search query report and seeing if any of your keywords are matching to queries which are irrelevant or unqualified. Negativing those queries out will improve your CTR and thus your ads' QS.
As I mentioned, I would not do this until your QS was 7 or more. You do want the top positions but not if it doubles your costs which a QS of 4 will likely do, whether you bid manually or not. Get that QS up first, even if near the bottom of the first page.
Therefore, you don't necessarily need to rank high to improve QS from better CTR. It's just a matter of having a better CTR for the spot you're at compared to what other ads would achieve at that exact same rank.
As I mentioned, I would not do this until your QS was 7 or more.