We self-tutored our dd for her St Michael's and Latymer exams last year (she gained a place at her 1st choice, and would have been given Latymer if it was our 1st choice too). There were four girls in DD's class who sat both exams and who were all home-tutored. All have gained places at their 1st choice school and only one did not sit Latymer R2. For us it was important to know what DD was learning and be able to have control over the fine detail as we were in a similar position to you with alternatives (as we live in Haringey!). Our problem with the tutor route was not knowing accurately dd's progress. Without speading paranoia how do YOU know she is good? That she is covering all the work required?
You state that she is good at NVR. That's really important for the Latymer test as it is tested in R1, and the top 500 or so (out of 1700+) progress to R2. When you reach R2 the chance of a place is about 1:2 because many people put Latymer as their 2nd choice (3 out of the 4 in our class who sat the tests did, and a scout around this forum will back it up) and the list moves down quite a way before allocation day.
There are lots of different publishers and online tests around if you fancy doing it yourself, and you already have set time aside each evening for 11+ work. This forum and the subject forums are fantastic for supporting home-tutoring - it made a HUGE difference to us
For NVR we worked through the Bond 'How to Do 11+, AE workbooks and the 'Learning Together' one. We then gave her a variety of tests, starting with the Bond assessment papers for 9-10 (it builds confidence and familiarity), Bond 10-11 (remember you don't need 'cube nets as they aren't in the real test), IPS 10 minute and full tests (the closest in subject and style to Latymer), Athey, Learning Together, and various online ones from this site and schools. We didn't set the actual papers until she could whizz through the tests, scoring (at that point) at least 85% in time (buy a stopwatch). Later on you can split the tests into 20 question segments to mimic the real exam which allows 10 minutes for each with no return. Rework weaker areas until she is confident. By October she should be scoring over 90% within time, and preferable higher, as they re-standardise the results on the NVR with soley R2 candidates
I don't know how your tutor can judge her against the Latymer English paper as the only thing available is the practice paper sold last year. There has only been one actual English test, and that was in November. DD sat that and found it different in style to the practice one they sold us. The real one (from her memory) had a not too challenging Comprehension (she felt it was easier than the St Michael's one the month before, and found it easier than the Habs Boys, Emanuel School, Greenwich and 'Schofield and Sims' book 4 ones). The Grammar was subtle. She remembers a question about explaining the difference between 'the teacher carried only the books from the room' and 'the teacher only carried the books from the room'. The Composition was a straightforward one about being lost....and she adapted a practice essay to fit the question. We asked dd to write essays on a number of subjects, which she could adapt - and it worked! We used some creative writing workbooks to help dd's writing skills as they had fallen behind (a succession of teachers were busy inproving the below average children). We spent almost every Saturday working on her writing and comprehension skills (her grammar is excellent) and she went from a 4b (easter) to 5c (summer) to 5a (christmas) as a result. The 'New First Aid in English' book is highly recommended for the basics.
With maths you must cover all the subject first. There is a Bond 'How to Do' maths book, AE tuition workbooks and the KS2 books in Smiths are also good. Buy some mental arithmetic tests as speed is important. Then onto the assessment and 10-minute tests. You could introduce actual papers towards summer (especially if your daughter is sitting the Sutton Mocks), but hold off on the Latymer ones until she is scoring well in the others as they require a different approach. DD only reached Q32 in her first Latymer paper before she ran out of time. She had scored 48/50 in a Redbridge mock Maths test the previous Saturday! After a few weeks practice she was scoring 44-46/50 in them and I then gave her Habs Boys papers which are of a similar level. Rememeber in the Latymer maths the average score in the exam is under 30/50!