Will not start when gears are not circled on dash?

Okay, so you replaced the range sensor on the transmission, correct? The description sounds similar to when the bushings in the cable ends fail. You shift it with the lever but the shift lever on the transmission doesn't actually go fully into gear because of the loose fit. There are bushings at both ends but the interior one is the more common failure point.
Try this test, Hold the brake or chock the tires, then release the shifter and put it in neutral or mid-range. Now have someone watch the transmission end of the shift cable where it attaches to the transmission. Now gently move the shifter inside the vehicle from say neutral to drive and then back. The transmission lever should move at the same time. With worn bushings it will delay and usually won't go fully into the detent. So, you shift to park inside. but the transmission end doesn't quite go fully into park and the range switch doesn't trigger the PCM to say it is in park. The bushings in some of the cables are replaceable and just snap in. They can be found on the Help parts rack in the parts stores. Another test can be done by removing the trim panel inside and then looking at the cable end as you move the lever.

Would that keep the selected gear from being displayed/circled on the dash? That is something I haven’t tried yet so I will try that and let you know! Thank you!

Yes. Say you put the interior shifter in park but because the bushings are loose the cable only moves the lever on the transmission a bit over 1/2 way into park. The lever on the transmission is also what moves the transmission sensor, because the lever doesn't move it far enough the sensor doesn't switch the BCM, so the engine won't start. Now you try to pull the cable back into neutral, but the lever only moves part way, and you have the same problem.

I checked that and the bushing is tight on the shift lever. There’s also no slack in the shift linkage cable.
The oddest thing about it all is there are some moments where it will start and then the next moment, it won’t. The only constant is if the gear isn’t circled on the dash, then it won’t start, if it is circled, it will start.

Okay, the circles are activated by the position switch. Pull that connector off and make sure the pins and socket are clean and that it fit's tight. After that the next step would be to look at the live data from the transmission with a scan tool and see if the switch is working but the PCM isn't responding or if the signal just isn't getting to it. I suspect a bad connection more than a bad module as modules in those don't tend to be intermittent. Maybe have someone move the connector while watching the indicator to see if it reacts.

Is the position switch the same thing as the neutral safety switch?

It's the one mounted on the transmission.