A couple of thoughts.
1) A SCR control is going to limit the on time for the element going to the skillet. In essence you run the skillet on "high" and throttle back the heat by reducing the power to the element via the SCR control setting (it pulses the power instead of it being on 100% of the time). This also limits the ability of a skillet to recover heat between batches of food. You are basically setting a governor on the the heating element. You could manually turn up the SCR between batches to recover the heat level and then turn it back to the desired setting when you add food if recovery time is a a problem.
Is there any heat level control on the skillet now or is it just on/off? I presume from your description it's on/off only. If it has an analog dial heat setting, you may can replace the control module at a reasonable cost. Typically these look something like this and the heat sensor is in the center prong. I've never modded one of these, but there is probably a way to modify the heat band with more precise components.
If you have this sort of controller, the ultimate solution would be to modify the housing so you can put a PID temp sensor in the center prong to read the heat level and use a PID to regulate the heating element. Yeah, it's a little more involved, but it's the ultimate solution (and it will cost more than just a SCR). Basically you would make (or buy) a PID module that had a 110v outlet, and using the shell of the above controller just to provide power to the element and house your temp sensor, plug that into the PID box.
But, back to the inexpensive SCR option....
I would consider using a different module and making a plug and play type of box for portability (and to be a little more kitchen safe). Instead of something on
Amazon of unknown reliability (ie, made in China), I would look at some of the products Auber Instruments offers.
You have several inexpensive options here. Analog SSVR (solid State Voltage Regulator) dial models run in the mid $20 range and just need the addition of a box, heat sink, power cord, and outlet to make the unit. A SSVR is basically the cousin of the SSR's we see all the time in smoker controls. The SSVR acts like that expensive analog dimmer you found, it's just a more modern product and uses a triac instead of a SCR to control the heating element. It regulates the voltage output just like a SCR module based on the analog dial feedback loop created on one side of the SSVR.They also have digital display models that come in the standard DIN sizes, where you have a percentage display instead of the analog dial.
Here are the options Auber has:
http://www.auberins.com/index.php?main_page=index&cPath=53
This is their least expensive option at $29.50 with the rheostat for 110v control, model SSVR25A. You just need to add a proper heat sink, cabinet, and the power cord and outlet to the cabinet to complete the project. It's rated to 25amps at 110v AC (with proper heat sinking just like a SSR).
http://www.auberins.com/index.php?main_page=product_info&cPath=53&products_id=332
Add a heat sink for $12.50
http://www.auberins.com/index.php?main_page=product_info&cPath=2_48&products_id=244
Add a cabinet of your choice (Auber also sells some of these), a power cord to provide power from the wall to your cabinet with the SSVR and then an outlet on the back of your cabinet to plug your skillet in and you are done.
Or you can hardwire the box with the VSSR in the middle of your power cord for the skillet if it's long enough and you don't care about using the VSSR with anything else.