Holy crap, what a pain in the ass this has been.
Step 1 was a stain that should have been the same color but because of the color of the wood it ended up way too dark.
Step 2 was me taking a chunk of an old door to home depot and having them match it. That got me a weird tan/orange color that you can see on the bottom of the door in this picture
Attached FileI thinned the paint so it wouldn't fill in the wood grain in the door. The color was close but it was too uniform in color. I decided to try putting the stain on after the paint. It settled in the grain of the wood and made the doors about perfect. You can see the test on the top of the door in the picture.
Here's a finished and installed door. The closet door on the left was the target color
Attached FileIt looks closer IRL but the LED lights make it look a little weird on the camera.