Is there a way to do a DFT with low latency and fine frequency resolution at low frequencies?
The answer is no.  You've explained some of the reasons why a DFT alone is not a good first step when trying to do low latency pitch estimation on low pitched human voices.  

Around the first DFT bin, the effects of the window and the complex conjugate image can interfere with just spectral frequency estimation, which a pitch of that frequency may even be missing.

But it may be possible to do pitch estimation with better resolution and latency than a bare DFT by using other methods (time domain, parametric, or composite, look for many other similar Q&amp;As about pitch estimation on this site).