Lag bolts vs wood screws for reinforcing garage door header

Question

I am about to install the garage door header bracket and I have almost everything figured out. There is a ~1 inch gap between the ceiling and joist I'm screwing into but I need every millimeter I can get to clear the rail and the door. I want to attach a 2x4 against the ceiling to add more working space. Originally I was just going to use a 4-6 inch scrap piece secured vertically with some 2.5" wood screws and then lag bolt the bracket into that as instructed. Now, I think I am going to remove the strap securing the wire and run the wire for about 12 inches so that I can fit a 12 inch 2x4 section horizontally across the top.

Should I attach the 2x4 with wood screws or lag screws? I'm worried that lag screws will require too big of holes that they will need to be positioned so low they might negate any reinforcement I might have had. What are your opinions?

Just so we are all clear with what we're working with here is a picture:

Answer 1

Jacob, here is my suggestion. I would use a 2x4 or 2x6" block at least 24" long. Then I would use some 3" construction screws. Make sure you pre-drill the block first. The screws should slip through the block easily. Then use washers. The construction screws look a lot like sheet-rock screws but are a lot stronger. They will have a Torx drive head. Use at lease 5-screws.