Filter bank for complex spectrum
Typically what you’ll see in an application like this is a polyphase filter bank, which is designed with a single low pass filter prototype. This keeps your prototype filter real, and they can be quite efficient in comparison to directly designing an entire bank of individual bandpass filters. 

The short of it is this is a multi-rate technique which aims to simplify the computational complexity while being mathematically equivalent to a direct implementation. By having only one prototype filter, the coefficients can be kept real and the filter is essentially frequency shifted N times in the backward DFT application after the polyphase filtering. This deals with your issue of complex conjugate symmetry in the frequency domain that you noted before.

This previous post had some questions regarding polyphase filter banks, and has a link to a really nice MATLAB implementation.

I’ve used filter banks like this in practice (my field is radar signal processing), where we almost exclusively work with complex IQ signals, so I can vouch for their viability in this application.