Instead of paper clip, try a used guitar string. Works for me and I just did it again. Shocking you can get the guitar string about 3 inches up there because of it's flexibility and the string winding provides a bit of cleaning. Hit it to brew with no cup in and the water is a yellow tint coming out. Just made a cup,,, awesome.
I even keep the guitar string in the corner of silverware drawer. If you're unfamiliar, choose a D or 4th string from someone 's guitar.