The MINIMUM filtration rate for canister filters is 4x the tank size. For a 300 gallon tank, the minimum filtration rate using canister filters is 1200 gph. Right now, you have enough filtration for a moderately stocked 175 gallon tank. For any large tank, a wet dry filter should be considered for biological filtration. I concur with Bderick67, either build or buy a large wet dry filter, and have, canister filtration totalling 1200 gph at the very least. Wet dry filters are fairly spendy, but are a simple DIY build.
Your 300 gallon tank is overstocked as is our 300 gallon tank. We have two 20" pacu, two large oscars and two 12"+ pleco. For biological filtration we have a 400 gallon capacity Pro Clear Wet/dry filter running with a CA-6000 pump (1560 gp). For mechanical filtration we use two spa filters fed by a Reef Flow Hammerhead pump (5800 gph), which is CONSIDERABLY more than the 1200 gph minimum. For redundant backup filtration, we are running a Fluval FX5 (925 gph) with a large 40 Watt UV sterilizer connected to it. From the very first day we have had excellent water parameters, i.e., ammonia 0; nitrite 0; and with once a week water changes, we keep the nitrate < 20 ppm. We have incredible, extreme mechanical filtration that quickly removes feces and debris from the tank. In the year that the tank has been running, there has been nothing to vacuum out of the tank. We chose to go without substrate for minimal maintenance. I am convinced that quickly removing debris and feces from the tank is what keeps our nitrates manageable.
In theory, you could add something like an FX5, which would get your flow rate over 1200 gph. However, your tank is overstocked, and that changes everything. I think at the very least, you should add a large wet dry filter and another big canister, like an FX5. (I say FX5, only because I don't know of another canister with a bigger flow rate) Keep in mind that even with tons of filtration, you can only get rid of nitrates (the end product of the nitrogen cycle) by doing water changes. (Unless you also have a denitrator.) At your stocking level, I think you will be doing multiple large water changes every week to keep your nitrates below 20 ppm.
What are your current water parameters? Ammonia and nitrite readings should always be 0. How much and how often you change water is determined by the nitrate level. You need a freshwater master test kit, and you need to routinely test the water. Here's the form I made up to record test results and how much water is changed out. If the nitrates were higher than 20 ppm, I usually retest the water after water changes.
The best way to purchase a freshwater master test kit is to go to Petsmart website and print out the freshwater master test kit info. If you take the printout in to the store, they will honor their online pricing of $13.49 versus their instore pricing of almost $30.
http://www.petsmart.com/global/product_detail.jsp