Mystery Wire solved! Maybe?The TCR of Invar36 is about 0.00117. So it is possible that the unknown wire is Invar. But this is just one parameter.
I have been doing some research and I do believe the newly infamous NiFe52, aka NienFethal wire I recently received from UnkamenSupplies and have been evaluating is Invar 36, also know as NILO 36, Pernifer 36, and Invar Steel as @TheotherSteveS thought it might be. We also do have some specks for it as put together by @vapealone on his "NI200 NILO Alloys" spreadsheet tab as NILO 36. The TCR value listed is extremely close to my testing listing the TCR value as .00118. My final TCR number was .0017 and what I have been using. You can find @vapealone's spreadsheet here:
High TCR Allows Listed as NILO 36
More information about NILO 36 here:
The NILO® and NILOMAG® Nickel-Iron Alloys
The Wire Wizard doesn't have it listed, but maybe @Dampmaskin can add it if gets a chance. This wire really isn't bad for TC and now if this is truly what this wire is called we can venture further for the adventurous. Another advantage is that its Nickel content is only around 36% so for those with a sensitivity or dislike for Nickel it may be an alternative wire to use.