How to Transmit Analog Signals Over Cable – Differential Transmission

At this low frequency it doesn't really matter whether they are routed as a transmission line on the PCB or not. The more important issue is capacitive coupling from other traces that could inject noise. You are only looking for a little over 10 bit accuracy, so nothing out of the ordinary needs to be done.

Some low pass filtering would be a good idea. You are sampling at 33 kHz, so clearly you can squash anything past 15 kHz, in fact that is a good idea. Hopefully you are super-sampling in the A/D and will then decimate and low pass filter later in firmware. This allows your anti-aliasing filter to be more easily realizable in analog. Let's say you've done that part right and really only care about maybe 1 or 2 kHz upper frequency. In that case, put two poles of passive low pass filtering at 5 kHz on each signal in differential mode. You need to put a little low pass filtering on each part of the signal individually because high enough common mode noise can fool active front ends and look like differential mode signal. The downside is that any imballance in the two filters on each line will convert some common mode noise into differential signal, so make these filters high enough, like a few 10s of kHz.

Should I be worried about reflections on the cable?

At 20 MHz the wavelength is 15 metres so a 1 metre cable is starting to get close to the problem area but I'd be more concerned that the LTC6363 is not going to deliver the goods at 20 MHz with a gain of 10 (20 dB). Look at the DS - it shows that it's fairly flat in gain up to about 1MHz then peaks up about 5 dB at 4 MHz then starts rolling off at about 6 MHz.

This effect will overshadow any relection nuances in my opinion.

The AD8132 that I now notice you are using (shame on you for not putting this on the schematic!) is a lot better but, still, at 20 MHz and with a gain of 20 dB there might be 2 or 3 dB attenuation and this will be of about the same order as the effect of relections.

Would a coaxial cable be a better/simpler solution in this situation?

Use shielded twisted pairs for best signal integrity and attach the shield to ground at the receiving end.