Don't change your bars or your stem just yet.

Move the shifters to the correct spot for you. See my photo below for what works for me.

(You may need new bar tape, but you can re-use the existing tape. It might be stretched too much from the portion at the old shifter location, but it'll work at least temporarily, and will likely be okay.)

Unwrap the bars (first, note which way it wraps) and undo the tape holding the cable housing against the bars.

Here's what I do:

1. Rotate the bars so that the ends of the drops are somewhere between almost level, or pointing down to a point about halfway down the seat stay. The curve from the center bar section toward the front is usually level or very slightly angled upward.

Fold the hood rubber to reach the clamp bolt, and loosen it enough so the shifters can slide along the bar.

2. In a doorway, sit on the bike, lean a bit into the door frame to stay upright.
I shake my hands loosely to get to a natural wrist angle, then bring my hands up to the hood location. I want the palm where I rest on the hoods to contact it evenly. And I check how my palms sit on the drops, and might rotate the bars a little to get it just right.

That's a small upward angle on the hoods for me. I added a green horizontal box to show the angle upward.

If the upward angle is too small, I feel like my palms are sliding/pushing forward. At this angle, it's neutral.

3. Check that both shifters are lined up with each other. Tighten the shifter clamps. Push the housing ends into the shifters to make sure they bottom out correctly. Tape the housing to the bars temporarily.

Go ride and see if it needs any more adjustments.

4. Tape the housing more permanently, and redo the bar tape.

New bars or stem?
Moving the shifters to angle upward will shorten the reach a little. If you still find yourself keeping your palms back near the curve behind the shifters instead of on the hoods, then you might want a shorter reach. A shorter stem and/or different bars. You should be able to easily ride on the hoods and have a small angle at your elbow, so your arms aren't locked. Locked elbows are hard on hands and shoulders.


My bars
The green box is exactly horizontal.

I have about 1.5 inches / 35mm of drop from the saddle nose to the top of the bar at the clamp. Riders with more drop will likely set their hoods more horizontal than this.

My fairly small saddle-to-bar drop lets me use both the hoods and the drops. (On a previous bike, I only used the drops on downhills or with very strong headwinds.) The drops are now my favorite rough road hand position, with more control and more comfort. And I'll stay in the drops most of the time with any headwind, or when riding with a fast-for-me group ride.