Components on both sides of one side PCBs
To be honest, I don't see any problems, though I have read the question twice now.

I don't even see any problems soldering the RTC, as an SO8 package really isn't that small, even for a hand made PCB.  What's your PCB production method?

To maintain good accuracy, you might consider keeping the circuit at a controlled temperature. You could use a Peltier element plus a thermistor to regulate the temperature.

There are such things as temperature compensated oscillators (TCXO) and Oven Controlled Oscillators (OCXO), but these don't seem to be available at 32.768kHz.