I've been out at Burnham Overy Staithe a few times, but in my older, less capable boat. Never had a chance to try the T38 there yet. Would be very interesting to hear how you get on.
Regarding getting out and pushing, I have, to my shame, first hand experience of this at Burnham. Due to a bit of ill-advised experimentation with the handling of my old Intex Mariner 3 (basically a blow up toy to which I had optimistically attached a 6hp engine!) I managed to nearly capsize and succeeded in throwing myself out of the boat. Lifejacket and kill cord did their jobs admirably, although I did manage to stick my leg into the prop before it stopped. Just a few parallel scratches though. Could have been a lot worse. I swam towing the boat and it wasn't far to reach the edge of the creek. By the time I was 25 feet from the bank I could stand which made jumping back into the boat a doddle.
That was on a super high tide. On the lower tides you really will be walking. And getting intimate with the mud.
luckily didn't dent my appetite for little rubber boats. I'm just a bit more careful now.... mostly.