First off - we went DIY for both girls - eldest did not make it (for nearest grammars) and youngest will be starting CHGs in Sept 2016.
Second - as others have said - there are no guarantees. Anything can happen on the day. Tricky question that they spend too much time on, nerves, illness, just not their day, etc.....
Third - competition - a lot of people are taking this exam and preparing hard for it - so you have to accept from the outset you can only do what you can do. Like you we were in no position to spend a fortune on tutors - so we did the best we can.
My view is that preparing for the 11+ is about aiming for a very high educational achievement which no matter what will put your child into a really good position starting secondary school. With little fish - she was definitely not the very brightest at her primary (and indeed they went on to the grammar schools) but she has turned out to be one of the brightest/ in top sets at secondary and it has given her a lot of confidence. Again - that never would have happened if we hadn't DIYed for the 11+.
Spelling - I don't think this is a huge issue. The exam certainly won't have spelling questions per se - there could be hang man style missing letters questions (cloze questions) - but so far these haven't appeared on the exam - only mixed sentences and word banks with fill in the blank. So more important they comprehend the meaning of complicated words and have the vocabulary recall to come up with a synonym or antonym than they can spell words precisely (because the answers are provided on the multiple choice exam and my understanding is that the choices aren't cruel - as in two similarly spelled words - effect vs. affect for example).
My advice to you is up the quality of the reading fiction your child is doing - that will be your best aid for vocabulary comprehension - reading list for 11+ here: http://www.elevenplusexams.co.uk/advice/english/reading-list
Make sure you discuss reading: meaning of words & implied meaning (so foreshadowing, word selection to indicate tension/ fear/ emotion/ etc....
Invest or borrow cloze workbooks - this is the area where tutored children can have the advantage - mixed sentences/ fill in the blank/ hang man style question practice is really helpful.
The rest is straightforward:
antonym/ synonym - often given an easy word you'd know and then a choice of 4 complicated words on the test
maths - sound calculation skills/ percentages/ proportions/ fractions/ - work on word problems
NVR - bond materials are fine for this. Don't worry about nets (the cube questions) - have never appeared historically in B'ham.
Finally - really work on making sure they absorb instructions and take the time to be really clear about what they're being asked to do. A lot of the near misses (and I include my eldest [little fish] in this category) come down to not understanding the instructions/ question/ what was being asked. I feel better to work accurately & steadily than to rush - box clever - if a question (say a word problem) is going to take ages - skip it and come back later. Better to answer straightforward division/ percentage type questions and then come back to the weird question about number of animals in a zoo - which is based on having 3 more than the number of giraffe's which is 5 more than the number of zebras which is 1/3 the number of geckos. There were 16 Llamas. [I've altered what was acctually there a bit but I kid you not].
Finally - just be openly proud about all the extra work, their improvement, the fact they're willing to aim high. What will be will be. Be hopeful but try not to make it the be all and end all. I think it's more upsetting for the kids if their parents are really disappointed - so prepare yourself to be incredibly happy & proud regardless of outcome for their benefit.
And as I said doing the 11+ (although not successful) has been a huge help to my little fish. Getting off to a flying start in secondary and being a big fish in her small pond has been great for her.
Hope that helps.