The external 32Hz clock trigger is worth a try, sounds simple enough.
For future reference, I found that I had to turn OFF particular device hardware and functions like WDT and BOR before going into Sleep mode or the unit drew too much current. It was a difference between approx. 150ua to a final 60nA while using the internal OSC set to 1MHz and 2 pins configured for IOC.
Looking at your schematic, I don't see any external loads that would cause the high current draw so my guess would be an internal drain.
The RTC CLKOUT looks like the simplest solution but now like you said, it needs to be pulled up.