So I made the jump to clipless and after my first ride, I think I need to adjust the position of one cleat. Does anyone have any hints about cleat position?

why do you think the cleat position is wrong? is it foot pain, knee pain, power transfer, clipping in & out, etc.?

typically, the cleat is position under the ball of the feet. i and many others suffer from hot spots, pain or numbness because there is too much pressure on the outside of the foot. the solutions to my clipless pedal challenges were:
1. Thin Sole from sole.com
2. Cleat wedges from bikefit

While my left foot feels fine, my right feels like I am standing on my toes. Both cleats are in the forward screw holes and as far back as can be. Can I move the right cleat to the most back screw holes and adjust from there?

Of course you can, provided that mechanical aspects are adequate.

There is no one, other than you, that can tell if it will cure your problems.

Maybe it will, maybe it won't. Try and see.

+1

When my cleats are too far forward on the shoe, I get foot pain and cramping on long rides (70+ miles). I had to move my cleats rearward a bit.