Definitely braid. Whilst I have no doubt loads of people still uses mono for pirking, thin braid means less drag, lighter pirks, more sport.
Don't forget shads and jellyworms are also successful for cod on those wrecks and generally can be fished on even lighter gear.
In my opinion, big tides don't make much difference to the size of lure required. You will obviously drift faster, but theoretically the boat, pirk and water are all moving the same speed, so you should have a vertical line for longer (theoretically).
Problem drifts occur when stronger winds blow in different direction to the tide. The wind pushes the boat one way and the tide takes the fishing gear another way. You soon have line streaming away from the boat - not effective for pirking.
Increasing the weight of the lure to unmanageable size is not really the answer.
Best to try shorter, more precise drifts, and lob the pirk ahead of the boat so you get it to the fishing zone before it has streamed away.
In this situation, thinner braid is a better option than heavy pirks.
If it's very bad, try jellies or shads as they can be fished more effectively even when the line is streaming away from the boat.
Enjoy Chieftain - it's an experience.
Pel.