Can you use Bartlett method in reverse? I'm wanting to do an inverse Fourier transform.
Can I use the Welch method to generate this inverse, by replacing the FT used within with an IFT?
Not really. Welch's method is specifically designed to estimate spectral density and discards phase information.
IFT and FT are almost identical and have the exact same complexity. If you want to do an IFT, just do an IFT unless you have a really good reason not to.