Hi, punkeson, and welcome to the Kent forum.
Your question makes perfect sense. The percentage pass mark for the Kent Test is calculated across all children sitting the Test, irrespective of residence, so across East and West Kent and all children who live outside of Kent and sit the test in a given year.
The only difference in outcome/opportunity based on area that I can think of is an 'in county: out of county' split in respect of 'headteacher assessment' by which a further small percentage of children are assessed 'grammar suitable'. Within Kent, local panels of headteachers meet to review cases put forward by their schools where the children have narrowly failed the Test and they take account of the respective school's submission of grammar suitability and of the half-hour written piece the child has produced during the Test. The writing piece is otherwise not marked. If children who live outside of Kent sit the Test, I am not sure that there is the possibility of a headteacher panel pass if they fail on one or more of the papers. (Someone will correct me on this, I'm sure, if I'm wrong.)
More children from West Kent than East Kent are entered for the Test and you are correct that over-demand for places in West Kent over many years has meant high competition and a culture of paid tuition and coaching to pass the Test. This problem is exacerbated by competition for places at 'super-selective' grammars in West Kent, ie, those for which an 11+ 'pass' is not enough: entry is based on ranked score or a combination of score and proximity to the school.
Kent County Council has done quite a lot in the past two to three years to work with West Kent schools to increase the number of grammar places and thereby reduce the distance some children need to travel each day to attend a grammar school. Weald of Kent has significantly increased its Year 7 intake (girls only) and, as you may have heard, is building an annexe in Sevenoaks. Judd and Skinners have taken extra classes of boys in recent years and Judd now allocates most of its places to local boys (although local boys are still ranked by score for the award of places.)
Of course, there are excellent grammars in East Kent too and hot spots of oversubscription exist outside of West Kent. The Council tries to anticipate demand, projecting five years ahead in its planning process. Each year it produces an education commissioning plan with a breakdown of supply and demand figures by district. This is available on the KCC website, and I think you may find it helpful. Let me know if you have trouble finding it and I'll try to post a link.
There is also an independent adviser who has a website providing very helpful news and analysis on Kent school matters. He looks at oversubscription figures for all the grammar schools - and other schools, secondary and primary - in Kent. Please PM me if you would like more information as we are not allowed to name his website here.
Good luck to you and your DD in your 11+ preparations. Don't be put off by the thought of other families going the paid-tuition route. You will see plentiful commentary in this forum on how to help your daughter prepare for the Kent Test at home, particularly through familiarisation with the test format and questions she should expect. It really is worth your time combing through past threads on relevant topics - go back 2-3 years; and ask questions if you need to: that way you'll feel well-informed and supported, as I was for my DS sitting the Test last year. (My thanks to all concerned!)