I was in your position last year, except I was renting rather than buying. I was planning to move to Tonbridge or Ashford.
This time last year the Kent admissions team consisted of 4 people who were literally snowed under with applications. The British government had moved school admissions from the care of school secretaries to LEAs but LEAs were not geared up for the extra workload, and Kent seemed to be especially unprepared.
I'm afraid that you are right about the process and that the risk is all on you: you will have to commit to a house and then cross your fingers that there are places in the school that you want.
Unfortunately it is a moving target and with all the things you have to do, you will be moving too slowly to hit the target. Even if you do manage to find a good school that happens to have children leaving so there will be places coming up that your DC could take, you will probably find those places gone by the time you've got the paperwork (purchase contract/ tenancy agreement) that will enable you to apply for the places.
This is what happened to me. In the end, I just found it impossible and I stayed in Surrey as it was marginally easier to move within the same LEA.
However, as a footnote to the experience, two of the good/ outstanding Kent schools I had been interested in, called me in September to say that some children had left unexpectedly and would I like the places now?
If you are really set on doing this move, then all I can suggest is that you go to the Ofsted website, put in a postcode of a house in an area you may be interested in, search for all the schools within 3 miles of that area and work methodically down the list calling the school office in each case. the call goes something like this (every single time!)...
"Hello, xyz school"
"Hello, May I speak to the person who deals with admissions please"
"Oh, they are dealt with Kent admissions now. Would you like the number?"
"Thank you but I've already got it. The problem is that I am moving to your area and I need to fill out the LEA application form. I was just hoping to speak to someone who could tell me if you actually have places in my DCs year?".
"In that case, you need to speak to Mrs X. She works on Tuesdays and Thursdays in the mornings".
99/100 schools won't have places but maybe one or two will.
After a while I was close to tears with all this. It took up all my time. required me to be extremely organised. Extremely polite. Sounding tearful helps I found, but by then I genuinely was close to tears.
Sorry. I hope it works out for you.