The position and appearance indicate that what you saw is M31. You've just
given an excellent description of the way M31 looks to the naked eye and in
binoculars. In a really clear sky, it jumps out at you.

In your telescope, you usually see only the central core, which is much
smaller. The object you describe -- about 0.5 x 2 degrees -- is just what
the relatively bright part of M31 looks like in binoculars. (The fainter
parts may extend out to more like 1 x 4 degrees.)

And M31 was only 5 degrees from the zenith at the time and place you
describe.