I ended up using counter sunk #6 screws and predrilled with a counter sunk bit which did the job nicely on the trim. I did not get them totally flush, it is a fine line between a satisfactory countersink and a huge hole which the screw passes easily through haha... I decided not to be to picky and be satisfied with satisfactory, they stick up probably a 32nd of an inch and I'm cool with that.
Note to self: go ahead and buy 1pc of extra trim for screw ups. It will be worth the $7 to have it sitting on your shelf forever than to have to hold the project up to order another strip if you booger up a piece.
OH... To make it legit, regarding the original post for the big screws; I used square drive deck screws. Gotta love the square drive.