Has anyone had any experience with a Tri saddle? I find that I ride up on the nose of my saddle fairly frequently and was wondering if the wider nose of the Tri saddle would be more comfortable.

It would not be comfortable. You need to ride with the sit bones on the wings of the saddle so move the saddle forward. If not possible with your current seat post- then look at an inline seat post that will move the saddle forward.

I found that on hills I was pushing forward on the saddle to get more effort in but I was literraly just perching on the saddle whenever I did this. I managed to move the saddle forward so that my knee is actually forward of the pedal crank which goes against normal setup but is the way I like it.

FWIW, my saddle is set so that my knee is in a relatively neutral position over the pedal spindle. Everything I've ever read or been told suggests that the knee ahead of the pedal will make spinning easier and behind will make climbing easier.