Oh, this nonsense again.
Yeah, I’m usually taking at least six weeks of vacation days each year just to deal with the garbage. It’s a real problem. 
Lucky for you that you don’t have a job to interfere with you getting there for the garbage collection times, isn’t it?
There are also collection points for dropping off garbage outside of the scheduled times/routes. The list for Taipei City is here, which I was able to find without being able to search in Chinese. I’m sure you can find the ones for New Taipei, in case you do end up getting a job.
Problem solved, then? Hope that helps.