I'm just wondering where to connect the grounding pin of the main power connector? Do I connect it to the center tap on the primary side of my transformers? (I'm using five)
Good Grief. NO to the center tap of the primary. AC power is not a balanced line (though I worked at a place where is was). The chassis is the most common place to connect the ground but in many consumer devices there is no 3rd wire at all and it can cause problems with units in other rooms. In those cases it makes more sense to isolate the audio / video / antenna cable with items designed for that purpose. It's not a good idea to 'float' the 3rd wire if supplied.
You need to think about connections to signal ground too, as somewhere this needs to be referenced to safety ground. This is a complicated topic, if you want both safety and good sound. Do a search on here - it has been covered in lots of threads.
The ground in North America serves to protect you from over voltage spikes, lighting and such. If tied to a metal chassis, it can serve to trip the circuit breaker if there is a 120V short to the chassis.
Signal ground can and often is connected to earth with no problems, so you can at least try it and see.