I didn't had a look on your data, but from what is told, I'm with altenbach: I don't think that FFT is the golden tool for you.
Uneven datapoints .. my fist idea was a sine fit , or more general: create a function with a sine a linear part, slice your data into parts with about 2 or 3 expected periodes, feed them into a LM-fit , ....
Greetings from Germany
Henrik
LV since v3.1
“ground” is a convenient fantasy
'˙˙˙˙uıɐƃɐ lɐıp puɐ °06 ǝuoɥd ɹnoʎ uɹnʇ ǝsɐǝld 'ʎɹɐuıƃɐɯı sı pǝlɐıp ǝʌɐɥ noʎ ɹǝqɯnu ǝɥʇ'