Hi carterusm, I've never used an official walk/run strategy. Kept meaning to try it, but on hilly training run (which is practically all of my long runs) it's simplest just to go for "walk the uphills". Even when training for the London Ultra which was less hilly, my walking/stopping breaks on my 26+ mile training runs were simply when I needed to read the instructions and check where I was on the map (and I had similar stops when following e.g. NDW or Vanguard Way).
For what you're training for, I'd suggest don't bother with a run/walk strategy unless you really feel you need it. Note: from my experience those Sunday runs are going to feel tough, particularly at first; you may want to start them at 6-8 miles and work up to 10-12 - and expect them to be slow.
For Thames Trot, which is much flatter than NDW etc., I'm thinking I probably ought to try a 25 mins/5 mins run/walk strategy on the day, and should try that out beforehand on a training run, but I've not yet had the opportunity(!) - maybe this coming weekend if my ankle is more comfortable and I decide to go for a 20+ mile run (I did about 17.5 yesterday, so I'm hopeful).