Personally I wouldn't disturb the filter for now, unless it's a long time since you last cleaned it and the flow is severely reduced or it's full of sludge. If you do clean it then obviously go gently and just rinse the media in water taken from the tank. The presence of a large amount of waste sludge will of course add to acidification.
Did you use the calculator I suggested to work out how much bicarb to dose?
http://www.dataguru.org/misc/aquarium/CalKH.asp?
You will probably need to add more than 2 tsp bicarb for a 300 gal tank. Maybe closer to 5 in order to get a significant KH and subsequent pH increase. Play around with some figures in the calculator first and you'll be able to see what sort of pH increase you will get for any given increase in KH.
It's much easier to work out if you know what your KH is - API do a test kit.
pH increase will be greater to start with if the tank KH is initially very low i.e. less than 1.
Unfortunately it's guess work until the pH gets off the bottom of the test range. Once it does, you'll be able to gradually add bicarb until you get the pH rise you want.
As your water is extremely acidic it may be the case that the bicarb will be used up very quickly at first, almost as soon as it enters the tank, in which case you may have to continue to add it gradually, a couple of teaspoons at a time (testing pH as you go), until you get a noticable effect on pH. I've never had to use bicarb on a tank with such a low pH so I can't say for sure. Just go carefully, testing all the way, and watching your fish closely for signs of stress. Good luck.
PS. Obviously continue with the daily 30+% water changes.