Yes, we visited in 2008 in our BK Sadler 29, draft 1.1 m. From the log, we went in about an hour before HW, and stuck to the outside of the bends, and there was very little water - occasionally only 10 or 20 cm beneath the keels. Weather was settled, calm and very hot, but with fog rolling in as we anchored. Once in, we anchored a little to one side, and dried out on firm sand. Beautiful spot, would like to go back, but a little nervous as the 290 draws more than the 29...
I've paddled the Avon in a canoe from Aveton Gifford to the coast (Bantham/Bigbury), then (after waiting out low tide) back again. That was quite a few years ago, and I don't remember much detail, but I doubt you'd get far up the river in your boat. There isn't much water at high tide, and not even enough for the canoe at low tide. Is yours a bilge keeler?
As I recall there were a handful of boats moored at Aveton Gifford, but they were all IIRC about 20 ft or less and lifting keel or shallow bilge keelers. I assumed that even those could only get in and out at the top of the tide.
I've also anchored off Bantham beach for the day in a yacht - calm, sunny conditions - and that was very pleasant, but never attempted to get into the river.
p.s. There was a thread about this, perhaps a couple of years or so ago, that might be worth searching for.