OP has striked all the right notes on the mum of West London Prep top set DD that preparing for the SW 11+ top schools: Aware of the exam format, external CEM select mock 6 months in advance, cautiously not having the past paper or full mock for DD to do at this stage. Try to balance between timed performance and undue anxiety but could also diminish their performance. Have gone through some essential exam technique for comprehension papers.
I sense the anxiety is possibly from the parent end.
There is some practical aspect to consider (in particular to maths subject) :
Grammar school like Tiffin first stage (DD didn't do Tiffin exam but we did sutton mock or similar grammar test) as well as CEM select exams, are multiple choice, timed pressure questions. Both exams are non adaptive and mostly equally weighted. These questions won't be extended questions like second stage papers. To get the best performance out of it is to get as much as questions that knows in a highly timely and accurate manner and don't waste too much time to few questions that stuck.
London consortium is also multiple choice but it is adaptive, so less time pressure but need to make sure no silly mistake for easy questions in order to achieve in higher mark.
Since grammar exam takes place first and then CEM select and Atom as first stage. It does make sense to improve speed, pace and accuracy on base / medium level questions as priority at this stage (including summer).
DD had done little maths practice until beginning of October last year as this is not our focus subject but this strategy did work in our favor for CEM and consortium test. Atom mock tests was our main practice ground (not customised test sets) we just randomly hit different schools (grammar or private) to practice.
We also did one CEM mock test 1 week before the actual test in end of Nov.
These efforts will not be wasted as it also build the good foundation for DCs second stage exam writing (typically happen in Dec and Jan for private schools).
In addition, although the CEM select past rate for SPGS (an other schools) is high (about 80% of the total applicants), it is unclear how much weight the result of this test will be taken account in the final decision. So no harm to try to get as high mark as you can.
As for the second stage, I think the schools (except consortium online) use written open format papers, in the paper there will be some extended "difficult" questions some where, normally the last two questions but not necessary so (SPGS make this easier as it divides the question into 3 different timed sections by difficulty). These questions are typical to identify candidates that has outstanding maths, not necessarily to be expected all qualified candidates to finish.
It is still, essential to finish the questions that DCs familiar with first. Since it is open format, writing down the steps and logical thoughts will help to get marks, but no need to overdone it, again only practice can improve this.
It is important to go through the exam techniques that bespoken to different type of tests above. But there is no need to spend too much time just talking about technique without actual applying it in a similar setting.
Be patient, progress take time.