Sounds like an issue with the FAD (front axle disconnect). Check the plug and wires. If you had a lift recently installed, the wires need to be freed up from the frame a tad or they will be too short and get pulled on causing damage.
I've never used a spreader and do it by feel but, you should have to tap in the shims. You can get a good feel for preload as well when pulling it back out. It shouldn't be crazy tight but have some decent resistance coming out. I'm sure you may have already done it but with the Dynatrac 44...
Starting depth is usually .042 on the JK is usually a good starting point and going up from there. I’d actually just try getting closer to .006 backlash before pulling pinion shims if you can.
And definitely redo the pattern doing what @CalSgt said. Adding pressure to ring gear really helps lay...
Definitely super close. Pinion shims make big changes using small amounts. So .037 to .045 is a big jump but, you are spot on with first too shallow and .45 looking a tad deep. Try taking out .003 to get closer to .042 and see what that does. Backlash is good.