Isolation of a signal in a frequency band
The algorithm I referenced is premised on the signal being a pure real tone, in which case it will give an exact answer.
The presence of noise or other tones will distort the answer somewhat, but the formulas are actually quite robust.  As long as the tones are fairly far apart (at least several bins), the distortion due to other tones is small.
Aligning your DFT frame so the main tone is roughly a whole number of cycles and a half has two advantages.

The parameters are read from four values of the DFT instead of two, so inherently more noise resistant.

The second harmonic will fall near a whole number of cycles and thus not have much leakage.


If necessary, your signal can be filtered (as you have done) to reduce the magnitude of the harmonics, but you need to know the frequency response of the filter to adjust your amplitude calculation.
Real world signals tend not to be pure tones.  The smaller the segment, the more it will resemble a pure tone.  The formulas I referenced (and am the discoverer of) have the advantage of being exact, so a large N is not necessary for better results.  In a recent job, I was able to take 8 point DFTs on ~1 1/2 cycle frames to calculate the frequency, phase, and amplitude to about 4-5 significant figures.
In radar jobs in the past, and the non-radar one just mentioned, the variation in the signal meant the results you get are dependent on your frame selection and how you choose to average your results.  The algorithm can give you nearly instantaneous values along your signal duration.
The derivation of the frequency formula can be found here:

Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT

This is an extension to three bins, which can be used if your peak is near a bin (&lt; 0.15 bin width) for more noise robust results.

Improved Three Bin Exact Frequency Formula for a Pure Real Tone in a DFT

In the pure noiseless single tone case, either formula will yield an exact answer.