Great to hear your thermometer is accurate. A rarity.
It will not work to just "Add a hotplate" for various reasons.
Of course you will need to run a 2nd cord from a SEPARATE circuit , but that's just the first problem.
Start w the insul, and let us know what result you get.
Is the cast iron skillet going to be the "chip pan" ?
If so, just drill and do the bolt legs.
But, a little cheap 8x8 cake pan would be best.
The mass of the cast iron will take longgg preheat time to initially transmit heat to chips.
I dunno what kind of grate you think you're gonna find, mostly because of the specific elevation of about 3/8" above element you need.
MAYBE you can find one w legs you can clip off to the right height, like on a cheap $8 grill.
That's why the infinite adjustment bolt legs are great, no matter what pan you use.
Course, w the bolt legs, after you have yer first 6 pack of Leinie's, you gotta make sure you don't rip the element out if you remove it.
I just take a handful when necessary and reach in and drop in pan.
Actually, best would be a small grate that YOU put the bolt legs on to height, THEN you can slide your pan to hotter or cooler parts of element, and not worry about hurting or touching the element after the Leinie's. Marc