Who knows temp control modules for glass melting?

Due to my association with one of the Hive, between yesterday and today I ended up picking up a bunch of kilns.  I'm gonna convert most of 'em for melting furnaces, but that's a story for a different day.
Today I picked up a bunch of smaller 120V kilns.  These are gonna be for the wife to use as she wants to get back into glass work stuff.

I don't know much about it, but from what everyone says for glass we're going to have to setup a feedback circuit that gets the internal temp from the kiln in order to control temp, and allow it to ramp down from X to Y and hold, then ramp from Y to Z and hold, then shut off. (maybe one more ramp and hold in there, again, not 100% on what glass needs to be stable while heating and cooling)
The only control on these things right now is what the kiln guy called "an infinite switch" which appears to just let you set the amperage through the coils then does your basic bang-bang control through bimetallic strips.  Thinking it through I would think that doing away with the infinite switch and plugging in a PD or PID controller would make the most sense, then I could just let it hum along and not worry about checking on it.

I can source the pyrometer through what my friends at USF use, but does anyone have any ideas of what I should be looking for in regards to the controller? I'm hoping to find something semi-generic as I know that use specific controllers can be pricey and considering I've got half a dozen of these little suckers, so I'd like to find something that is relatively cheap.  Ease of programming it would be appreciated as well.  

You're looking for a Programmable Temperature Controller.  I like the OMRON stuff.  

It's been a while, but the ones that were used in the studio I used to work at didn't look overly unique.  

Look up Orton, that is who makes all the controllers on my kilns.  A lot of manufacturers also use their stuff and rebadge it. Fully programmable for what you want to do with temp ramps going up and down.

Omron, Omega, Wattlow and plenty of others make PID temperature controllers that should do what you need.  

Here is the Orton on our glass kiln. Pretty basic compared to the ceramic kiln controllers but it does what is needed.

I use Bartlett controllers on my ceramic kilns. https://www.bartinst.com/kilns/1

There are basic PID kiln controllers on eBay that you can use to trigger the relays but most of those are lacking flexibility. I've wondered about setting up a RaspberryPi to control my kiln, but considering you can find actual kiln controllers for a few hundred bucks, it just wasn't worth the effort. 

Here's a guy who designed and built a line of heat treat ovens.  Talks about all the details including the temperature controllers.

https://www.youtube.com/playlist?list=PLvITyjNApwrrvtJUl50swrNli7VUzIEnE