Should I register my car in Missouri?

Last week I bought a used car. I got a title. I moved to Missouri in January, and I'll be moving back out of Missouri in a month. I have insurance on it. I've been looking at the papers I still need online, and at reviews of the different office I need to go to. Apparently, I need info from the assessors office to show that I'm exempt from property tax on the vehicle or to pay it.

It's gonna be an hours drive to get to the office. They dont have accurate info online on hours open, they don't answer the phone, and the voicemail says that they hope to open again on April 4th. It's April 15th. I figure it's gonna be another drive to get to DMV offices, and reviews on both offices show that there's 2 hours waits, and extremely unpredictable closing times. So I'm looking at having to take at least a day off of work, maybe more.

I make like $300 on a good day. The max fines for late registration look like $200, and for the traffic violation it's $50.50, if I understand right from my Google search. If I were able to even get a hold of somebody at either office during business hours, I'd go ahead and register. Honestly though, I'm struggling to justify the opportunity cost. I could get caught and fined twice in a traffic stop before it would be worth doing it.

Am I missing something? Is it financially worth registering my car? What if I just register when I move, in the new state?