Andy_K 

It sounds like you've got a fit issue, but I think there's a good chance you can fix it with your current bike.

Bike fit is all about balance. If you're putting too much weight on your hands, it's because your balance is tipped forward. Higher handlebars aren't the only way to fix that.

Picture the triangle formed by your pedals, your butt and your hands. What you want is for your weight to be perfectly balanced across a vertical line drawn up from your feet (actually, the bottom bracket since that's the center around which your feet are moving). You've got too much weight in front of the line, so what you need is to move some behind it. Sitting more upright does that, but there's a point beyond which raising the bars more is counter productive. Other options are bringing the bars closer and moving your butt back.

One of the sacred rules of bike fit is that you don't fix reach problems by moving the saddle. However, like most of the rules of bike fit this one has some caveats behind it. You should never move the saddle forward to get closer to the bars (because it tips your balance forward), but it's OK to move the saddle back. What's really sacred here is the space between your hips and the bottom bracket -- you have to give your legs room to move -- but there's an arc of acceptable positions that have the same distance. If you move your saddle back a little and down a little, you keep the same distance from the pedals and gain some rearward balance.

Having moved the saddle back you may now need to lean more to reach the bars, which defeats the purpose of moving the saddle back. To fix that, you might need a shorter stem.

Do you see what I'm getting at with all this? Bike fit is hard to do in text, but if you understand the basic concepts you can do it yourself. Otherwise, some pictures of you on the bike might help. A visit to the LBS might also help.