Baseband OFDM Implementation questions
You're describing DSL.

So, go and implement DSL! The common ADSL is an OFDM system.


  This being baseband is there a way of not having to use quadrature mixing to transmit the Real and Complex parts of the IFFT i.e. non-passband way of sending it?


Yes, you can just make sure not to use one half of your carriers. That's mathematically not different from using a half as long DFT and and shifting it up by half-bandwidth.


  I am trying to keep the demodulation part as simple as possible. Anyway I can get away with not using channel estimation i.e. non-coherent demodulation with DPSK or something similar?


I don't understand that question. OFDM is used exactly because you'd need an equalizer to use a broadband channel, and the channel estimator is OFDM, in essence.

Yes, there's OFDM systems that use a differential modulation on their subcarriers (namely, DAB/DAB+). The rationale, however, is usually a tradeoff between achievable rate and easy implementation: DAB has to deal with doppler spread, anyway, so it would require a significant amount of channel sensing if done non-differentially; if you're wasting much SNR on channel estimation, you can as well spend 3dB of BER curve and do differential modulation, especially if you're in the early 1990's and everything else would be computationally hard.

If you're doing fixed line communication, where the channel rarely changes, using a differential modulation is very inefficient compared to having a channel sensing preamble. You'd need to build a system with a higher bandwidth to achieve the same rate you could do with channel sensing, and that in a channel where you really want to avoid being forced to use higher frequencies.


  Any pointers to fully implemented systems that I can dissect to learn more?


ADSL.


  Considering the low data rate, I'll probably end up doing this on a low-end DSP.


... end up using existing DSL link technology instead of building this on your own.

I honestly don't think the modulation is the hard part here – the link and network layer becomes interesting. Twisted pair for a couple dozen meters sounds like you actually just want to use 10/100 Base-T. Modern network cards are surprisingly good at dealing with low-quality channels, and shielded twisted pair is actually a pretty nice channel (as opposed to what you claim, similarity to powerline).

If you really don't have the chance to implement half-duplex 10Base-T, you could probably simply go, physically, for simple serial RS-485; again, the problem is likely less a physical, but network layer design effort.