lendog,
You can use the 2 x 4 supports that are on edge that support the 3/4″ plywood bar top. If your worried about splitting the 2 x 4 just make pilot holes slightly smaller than the diameter of the screws being used. You can even add more 2 x 4 supports to give you more fastening points with any scrap 2 x 4 pieces you have.
Also,if you don’t want to use screws that that are longer. Just bore holes a little larger than the screw head half way through the 2 x 4 on edge. This will countersink your screw. Easier to work with shorter screws. Remember to measure how much your screw is countersunk and subtract that from the length of screw now needed. Better to be a little short on the screw than having the screw come thru the laminate top because it was tightened too much.
You also do not need to make a pilot hole in the laminate top. Many of us have slipped and have had the drill bit exit the top !!!!