My daughter went through the awful 11+ process this year and I SO sympathise OP!!!
The thing with my daughter is that, although she's at a North London prep, she's not the brightest tool in the box and definitely no high-flyer. She's extremely average in academics with English being her worst and Maths her best subject. Verbal reasoning was a killer for her (and me!). She had lost motivation to prepare for the 11+ pretty early on into the start of year 5 and all the best laid plans of a year of preparation went out the window with covid. 11+ prep became a battle-ground at home and I just gave up and left her to go to the tests as unprepared as she wanted to be (for the sake of my own sanity).
My parents were telling me to not even let her sit any of the tests, as rejection will be awful. But I thought that given that all her friends at the prep were doing the 11+ she would feel even worse and lose all confidence if I didn't believe in her enough to even let her sit the exams.
The one good thing about my daughter is (given that she's generally not fussed about academics) she doesn't get nervous before assessments, has a lie in and is pretty laidback about it all. She's also quite a lovely polite girl and interviews well (not sure what weight that has though).
So my tactic was to apply to as many schools as possible including some of those that have lower entrance criteria and are considered "back-up schools" in the hope that at least one school will accept her and she can be proud of herself and gain more confidence in her abilities /motivation for learning. My expectations couldn't have been lower though. We also didn't go for completely hopeless academic schools like Habs or Henrietta Barnet or schools that had a second round (because it would have been awful for her if her friends were invited to the second round and she wasn't).
Between October and January she must have sat about eleven 11+ exams (grammar and indie) and I signed her up for a few art/drama/dance scholarships so she had to do those tests/interviews as well. She saw it all more as an inconvenience rather than anything stressful and bizarrely actually enjoyed most of the interviews (an opportunity to talk about herself).
At the end, she didn't get into the top-top indie schools like Highgate and is sadly too far down on the waiting list for the grammars, but shockingly got offered 5 indie schools (including a 10% fee-reduced art scholarship at one of them) and is 3rd on the waiting list for another indie school. All those 5 schools aren't considered to be top academically but are still great schools (Aldenham and Queenswood being two of them).
Now my daughter is super proud of herself and I think this has given her a boost to think that she can "do it".
My approach was not to tell her about rejections (lie to say she got onto the waiting list) and really talk up the schools that offered her a place.
I agree it's a completely horrible unfair system though OP!!