I am processing a video of the total eclipse and I figured it would be nice if I slowed down the video right around totality. Is this possible?

Slowing down footage always comes with possible issues because you will need intermediate frames that are just not there.
You can use kind of a frame doubling, that's what LRTimelapse offers in the render dialog, there is a "Speed" setting, which you can use to slow down or speed up your video. This is certainly the easiest way.

The more flexible way would be an video editor, like Davinci Resolve or Premiere. They offer more options, like frame blending or even try to "invent" intermediate frames ("Optical Flow"), This works more or less well depending on the footage. Also they offer to keyframe the speed to make so called "Speed Ramps".

I'd use the new 'AI' Smooth Slow-mo in Final Cut Pro 10.8 on a section of the timelapse you want to slow.

Nice! I wish I had Final Cut but it's too expensive for the few videos I make.

Go for Davinci Resolve, there is a great free version with very few limitations in comparison to the payed one.