I know this has to be the way I'm positioned, but at the end of my ride, my left hand is numb and my right bicep/tricep is very sore. The opposite (right hand, left bicep/tricep) are fine. I know that I must be putting unequal pressure on them, but for the life of me I can't figure out what I'm doing or how to correct it to more equally balance my weight.

Sorry for the dumb question, but are your handlebars straight?

What type are they?

Maybe a better question would be does your bike veer to one side or the other when the handle bars are straight? I'm just wondering if your wrists and muscles are sore because you're fighting to keep your bike from turning one way or another.

Usually uncomfortable hands are a sign of handlebars that are too low. The lower your handle bars the more weight you shift forward on your hands & arms and smaller & less supportive the seat you require (since there's less weight on it). The higher your handle-bars the more upright your body position and more weight you shift to your seat, and hence you need a bigger seat else your butt will go sore & numb. Maybe you have a long torso, that shifts weight to your hands/arms. I find comfort & speed do not mix, the most comfortable is upright sitting and the fastest forward and low... somewhere there's a balance for you.

I can't really answer why you have a sore arm, I can't say I've ever had sore arms from biking my hands are another story when I'm riding a bike with a straight bar or a road bike where I'm low and a lot of my weight is forward on my hands my hands kill.

What bike do you ride. How long are the ride?