First I have to ask how big you are. What is your wingspan? You say your drawlength is 31-32 inches. Well, which is it. It's not either/or. To have anything close to a 32" drawlength you'd have to have a wingspan of about 78", assuming you're shooting fingers; 80" if you plan to shoot a release. Measure your wingspan and divide it by 2.5 to get close. If you will shoot fingers then add an inch to this.
Now that this is done let's figure out some bows. Without naming particular bows you want something with at least 38" axle to axle (A2A) length; preferably longer. A brace height of at least 7" and closer to 8" is even better. A bow that peaks at 60# is plenty for any whitetail or other animal walking this continent, and is more in line with what you are shooting now.
You can go to a shop to look at some bows and/or check some manufacturers" websites to see what they offer. Then go to the shop and see what they have. Don't be surprised if you don't find many longer bows. The latest rage is short and light, which isn't the best IMO.
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Carbon arrows will definitely help you pick up some added speed, possibly as much as 30fps. There is nothing wrong with using some of the gadgets (sight and such). Regardless of what some may think archery and bowhunting in particular is not a GAME. If something such as a sight and stabilizer can help you shoot more accurately then so be it. You owe it to the animals you hunt to be as accurate as you can be. Believe me, there are very few people who can shoot instinctively with any consistency, and those that can either do a lot of practicing or just have a knack for it.
Lastly, if deer are jumping the string on you it's not because your bow is slow. It's because your bow is noisy. They react to the noise by preloading their leg muscles to run. This makes them drop to go. Get the bow more quiet than it is.
Anymore questions?