Interesting.
But we may need to consider density as well to make the equation even more interesting

(Density of Ni200 is two times higher than Ti1 isn't it? If yes, specific heat of a TI wire is actually lower than same gauge/length Ni, right?)
Besides I have carried out a stupidly inappropriate experience myself: running the very same Kanthal/Ni hybrid coil both on Ni and Ti settings on the beta.
In theory, TCR/TFR should be very Ti-ish of the coil I have used and indeed it worked (and still working) as supposed on Ni mode but on TI the universe broke

I had to set temp settings extremely high to get anything out of it. And again: very same material very same setup and way off temp offsets.
So for now, I stick with Ni mode .
Ps: we are always referring to Ti TFR curve however I guess that quite a few of this curves are actually simply lines like Steam-engine's one. Ok, technically it is still a curve with zero curvature. Either way, using constant TCR as an approximation means a simple equation should give an acceptably accurate temp value