Size of pilot holes for 1/4" screws in transom?

I'm installing a trim tab, and have one pilot hole drilled so far (which I probably need to redo since it's offset, as I wrote in another thread).

I'm using 1/4" pan head sheet metal screws, and what I've read is that I should use 3/16" pilot holes. (The MB trim tab kit itself had no instructions.)

But when I tried to screw the screw in, it stopped with about 1/8" left to go, even with my corded drill. It was so tight, the drill couldn't back it out, and I had to grasp a screwdriver with a pair of pliers to do it. The pilot hole was longer than where the screw got stuck.

So, is 3/16" really the right diameter pilot hole for 1/4" screws, and I'm just doing something wrong? Or should I drill thicker holes, such as 13/64" or 7/32" or 15/64"? I will also be using 3M 5200 adhesive sealant.

In this video, the guy is just using a screwdriver... there's no way that would be possible in my case: http://www.youtube.com/watch?v=cV2BKm1s0iQ

Thanks.