Here we go again – would that not be a case of borer, even WITH a kli revii? I am not questioning your rov’s p’sak, but it still makes me think. UNLESS – the water and coffee going through the filter is considered the tov, and the coffee grounds are the ra, so the liquid being the good part MAY be separated from the bad part of the grounds that remain in the filter. Interesting.
In the summertime, I used to brew double strength coffee (like tea sense) and just add hot water the next day. It was decent, certainly better than instant. I also experimented with using a thermos to just keep the hot coffee hot overnight for an early morning coffee. It was OK.
It takes literally 30 seconds more to make brewed coffee with a filter than to make instant, and it is SO worth it.