I always book two one-way tickets. I started doing that when I was using miles as you needed to get miles seats as soon as they were available. Since my trips are 3+ weeks, I couldn't wait three weeks to get a round-trip on miles as the outbound would no longer have any decent seats available. Now that miles seats are so hard to get or are routings I don't want, I still do two one-way tickets. Last time I priced a round-trip ticket, it was $800 more than the two one-ways I had purchased . . . at least at the moment I was doing the search.

I also always use a private or incognito window when doing my searches.