Well, honestly, I'm going to go with the 3/4". I haven't played with the HPDE specifically, but I've read that it's not quite as stiff as the equivalent plywood. I don't think I'd be comfortable with anything less than 1/2" and I'm not going to try the 1/2". When I did my prototype platform, I not only narrowed it and lopped off the corners as much as possible, but I also lengthened the platform--so I have extra length that extends past where I have platform braces. Because of that I was hesitant to do anything too thin.
HPDE is basically the same stuff you'll see on the plastic cutting boards. So think if a 1/2" cutting board would do the job.
That said, if you were really determined to use a thinner material, you might be able to get away with it if you add material to your braces. maybe form a "frame" underneath the HPDE out of aluminum flat bar to provide extra support. However, by the time you factor in the costs of extra bracing materials, you're probably spending more money than had you just gone with 3/4" HPDE in the first place.
Now instead of HPDE, you could certainly go with marine plywood or even regular plywood. Give it as much of a waterproof coating as possible and slap some closed cell foam on the top and you're done. If it only lasts a few seasons, then just make another one. That's a thought.