I believe you are good to go as is. However if this is going to remain on your mind, then I think Lee's concept is the simplest & would add a good deal of strength. What I would change though is use a wood screw that is #10 with the head of the screw buried in the c'bore, as Lee suggested, but take it one step further and that is to make a couple of plugs of the same material, glue into the c'bored holes with the grain orientaion aligned with the adjacent grain, then sand flush.
Thoughts entering one's mind need not exit one's mouth!
As I age my memory fades .... and that's a load off my mind!
"We Live In The Land Of The Free, Only Because Of The Brave"
“The problems we face today are there because the people who work for a living are outnumbered by those who vote for a living."
"Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." Winston Churchill