Also, why is it that we are limited to the most basic FFT resolution, 2x overlap?

When they talk about overlapping FFTs, all they mean is that there is more than one FFT and that each FFT is operating on a different time window.

To do a 4X overlap, you could create a second FFT module (which already does 2X overlap), and delay its input by 1/4 of the FFT length. Now you have the spectrum at 4 different points in time.

Next take two iFFT modules, delay the output of one relative to the other by 1/4 the FFT length and add their outputs to recover the time domain signal.

To do more than 4X overlap, just repeat the process, using 1/OverlapNbr as the delay.