Why are you so interested in a school that so obviously discriminates against state school pupils in entrance exams.
In the two senior schools that my own children are both, both have about 50% of their 11+ pupils from state schools. That is a lot of places open to state school pupils.
Neither school publishes their entrance exams because they are not content specific, and one of these schools is selective and the other not. They both use NFER papers, and then ask the candidates to write a story based on a title or opening sentence, along with a speedy mathematics paper. If pupils are doing SATs, they shouldn't have a problem with an entrance exam.
As for preparing for NFER papers, you go to WH Smith and buy some Bond Assessment papers. To do about 3 of these papers is enough to prepare for an independent school assessment. At my boys' prep school, they would do these silently for about half an hour a week - no teacher input at all.
If grammer school tests require intensive coaching, that is hardly the fault of independent schools. There is probably a fear factor in grammer school entrances where parents don't want to take a chance so will do whatever it takes, even if there is no evidence of added value. Plenty of bright but otherwise ordinary kids get into grammer schools without coaching.
Both independent and grammer schools would prefer that the 'real child' is presented on the assessment day, rather than one coached up to the gills. Neither type of school wants to select the wrong child who may struggle with the real work.