Thanks for share the data!
Just make a correction, N1 doesn't goes up and down with ATM as actual temperature. Once you use ATM over refTemp, N1 always lower than what current temp's N1 would be.
For EPR controlled Engine like PW and RR, you only need to get EPR, and let EEC to tell what N1 should be, but for N1 controlled engine like GE/CFM, there is a more complex 3 tables (on 737 at least as I know) to look for correct N1 (I guess that's why it doesn't work well on the 767GE expansion, though I didn't bought it so can't tell)