I have a slightly different experience with getting LL in HS for later in the day that I haven't seen discussed. In mid November we planned LL at HS but couldn't be in the park until 4:30pm. At 7am, I got SDD for 7pm. At 11am I wanted to get RnRc or ToT for around 5 but the times weren't out that far yet. I can't remember what times were showing for MFSR but we didn't care about getting LL for that as we often ride single rider. So I kept refreshing for a few minutes but the times were still too early. I ended up having to wait until 12:15 to get a LL for ToT after 5pm. Thankfully I was in a place with good wifi and I had time to search, although it was a pain to keep checking back every few minutes. However, the thing that got me was that I wasn't eligible to get another LL until 2:15, not 1:00 as I had hoped. I think at 4:15 I ended up getting RnRc but I had to do a lot of refreshing to get a 5:30 return as I wanted to have a time close to ToT so we could knock them both out in a row.
People hardly ever talk about not getting late enough LL choices at HS. Maybe back in November, there weren't as many people using
Genie+ yet. The parks weren't too crowded that week either, so that probably made a difference.