When I was diagnosed with it I spent a week to ten days doing the eccentric exercises twice a day. I didn't run in that time, just used the exercise bike to keep up fitness and to stop me piling on pounds (The exercise bike didn't cause any discomfort to the achilles). I also iced twice a day, 20 mins on a bag of frozen peas!
I then started with slower paced runs, but only had one month to prepare for my 11 mile trail race. I had no intention of pulling out (it was a charity team relay!). So once I could run with a moderate level of discomfort I did start increasing my mileage and intensity. The one thing that you notice with achilles tendonitis is that it is most painful during the first mile or two of a workout......this puts off many people from continuing, but the more miles I did, the more the pain disappeared during workouts.
It'd always be terrible again the following morning, but it seems to improve over time with those eccentric exercises.
Another trick is to watch heel striking, that seemed to be the cause in my case. Its hard to adjust but try to land midfoot if you can........
As for building up to half marathon distance, I'm guessing that your basically after completion rather than an actual time goal? If you just need the distance, I'd say that if you can complete 10 miles in a training run without feeling like you're going to die, you'll probably manage all 13.1 on race day under competition and race day adrenaline. If its any help, when I was underconfident about my ability to finish certain distance races a few years ago, I'd hide a bottle of lucozade sport in a hedge a few miles from the race end.........but you might find that there are marshals with drinks for the competitors too.
