You do not want a backing plate on the mast step. The day may come, hopefully not, when you may loose a shroud and get dismasted. Screw holes are easy to fix but take a chunk out of the cabin top where the mast sits and you may as well ditch the boat. From the photo, I could not tell what I was looking at but Clark pointed out it looked like an interior cabin shot. I would not recommend that the mast step be even through bolted. The purpose of the mast step is to keep the bottom of the mast from sliding horizontally. The forces involved are minimal and mainly when the mast is stepped or takn down. That is the reason why short wood screws are usually used. Once the mast is up it is pressed to the step by the tension of the shrouds and only requires light anchoring at the step to stay in place. Those long bolts you have there are not doing much and could cause quite a bit of damage if ripped out. You could pug the holes from the inside cabin and fill the holes from the top with an epoxy. Before the epoxy dries insert wood screws that will get some bite into the wood. I would say 1" long screws would be plenty. We take trips on a trailerable Starwind 223 and while sailing in the Chesapeake Bay going to St. Michaels we had a structural failure (suspect a failed clevis pin letting loose a shroud) we lost the buckled mast overboard. At the cabin top there were four shallow holes where the mast step had been attached. Since it was an accident the insurance company paid for a new mast and riggin and the holes were filled in with an epoxy and wood shavings new slightly thicker screws were used and the step was attached prior to the epoxy setting. That was around 7 or 8 years ago and it still going strong.