A UPS wont smooth the wave to my knowlege.
And yes just put it as a load after the smart shunt. That way the system will keep the correct SOC.
As far as i know the humming wont damage anything. I have a few longer serving systems with strange noises that are load related and so far (more than 5 years) no issues to date.
When you are sizing your other little one, just be aware of its power factor. And size the inverter larger.