The real lead is buried here.
@RetroGamer_74 posted a version of the "launch into HBL" step by step (the wait five seconds, hit home part) on his github page, that has me currently on 3 for 3 on HBL launches after coldbood - using the HBL DNS (have ESP8266s lying around, but those are occupied at the moment (not for PS4 stuff)
).
Also - the step by step he layed out is faster, and has fewer button entries than what I used to do in the past.
So major props for that.
Link:
https://github.com/RetroGamer74/ESP8266_Homebrew_2.0_Switch_Pegaswitch/blob/master/README.md
If the "five seconds, hit home" method turns out to be a more reliable way to launch HBL thats worth quite a bit, because it has the potential to half the mocking around time in the menu, before getting anything launched.
edit: 4 out of 4, ... seems pretty reliable to me...
So the trick is (regardless if you use the ESP8266, or just the usual HBL DNS) to press OK on the "will now be closed" prompt, as ususal, then wait 5 seconds - then hit home, then after another 6 seconds you'll be on the main screen, where you can navigate to the gallery and start HBL.