After much trial and error, I think I finally figured out the solution.

Even though I could get better prints by tweaking with the temperatures, I could never totally eliminate the problem. The better I made it look by cooling down the bed, the more likely it would break free and the print would fail completely.

At one point though I happened to print something taller, and interestingly enough a similar band of ugly layers appeared higher up in the print as well.

So I started a closer inspection of the Z axis rollers. The Ender 3 has a funky setup where there are 3 rollers at each end of the X axis. Two are fixed and one can be adjusted to change the tension of the rollers against the Z rails. What I discovered was that a couple of the non-adjustable rollers weren't terribly tight and could be turned by fairly easily with my fingers. At the same time, the adjustable rollers are starting to wear a groove.

On a hunch, I decided to try re-adjusting the tension so that I could no longer turn any of them with my fingers. It definitely had an effect...now the bed was too high and it would no longer extrude the first layer because the nozzle was too close. This required going through the complete bed leveling process to get it back in spec.

Once I got it re-leveled, low and behold it's printing like new! The height is coming out spot-on too.

I suspect what was happening is that the rollers were too loose and at certain heights they we allowing movement in the Z axis. Perhaps there is a flat spot that was allowing the X rail to droop, then once it got past the flat spot it would print cleanly again.

I haven't printed anything tall enough yet to see if the bad layers still show up higher in the print, if they do, I think it is probably a sign that I need to replace some rollers. In the mean time, I'm thrilled to be getting decent prints again!

Update: This ended up NOT being the solution to my problem. However it does seem to be related. As I mentioned in the comments, the problem returned after a few days of the printer sitting unused. I have since been able to get it printing better by going the opposite route - loosening up the Z axis bearings. At the moment it is printing somewhat better, but still not perfect. I am also having under extrusion issues when may or may not be related. I have ordered some new rollers to see if that helps since some of them had a pretty good groove worn in them.

Another Update: I replaced several of the Z rollers that had become grooved with some that claimed to be a little harder material. So far this seems to have mostly cleared up the issue. I have now completed several large print jobs and the first layers have been coming out pretty good.

I also ended up taking out the Capricorn tubing on the extruder. The extruder skips were becoming quite bad and causing under extrusion issues throughout the print. The Capricorn has a little smaller inside diameter than the stock tubing and I wondered if it was too tight on some filaments. I went back to some plain white cheap PTFE and that problem mostly went away as well. I still hear the "click" once in a while, but it is fairly rare. I may try tweaking the motor current a little to see if I can get rid of that. All in all though, the printer seems to be printing about as good as it ever has.