Auto/Match Total Exposure being thrown off by bright spots (the sun)

Do you plan to do time lapses regularly, or is this more of a one-time project?

If you aren't going to do time lapses very often, then it's probably a good idea to try richardplondon's idea of doing a temporary batch crop just to get a better result out of Match Total Exposures, then doing a batch reset of the crop afterwards. My impression is that Match Total Exposures is designed more for relatively similar exposures, not wildly dramatic changes like night-to-day.

If you want to do many time lapses of this type, you should look into time lapse software that works with Lightroom. Many of them, such as LRTimelapse, have specialized features to smooth out day-to-night or night-to-day time lapse transitions. They aren't fooled by the sun going down or coming up, and so they work very well. But those applications usually aren't cheap, so they may not be worth buying for occasional use.

I believe you will get more consistent results if each photo is cropped to exclude the sun itself.

AFAICT the current cropped area only is used for analysis (whether by 'match exposure', or by 'auto tone', or by 'auto WB').

You'll still want to include a representative proportion of sky and ground etc; so this is more an art than a science.

 Afterwards you can Reset the crop for each photo, to show its full frame again.

At least one timelapse plugin exists which can smoothly increment exposure adjustments through a sequence. This works best on the basis that unchanging exposure settings have been used in the camera. But if the camera has been allowed to auto-adjust its exposure in response to its live metering of the changing scene, that approach is not so useful; each frame must be independently evaluated against some desired aesthetic outcome which only you really know; and which the computer cannot be made to truly understand.