There appears to be plenty of room to make a new hole and put a
strikeplate back in. This doesn't solve the second problem of the lock
becoming engaged through repeated door openings and closings.

Get a decent lock. Yours is cheap and/or worn out.

Get a Schlage. Don't mess with the cheapos like Kwikset, or you will be
right back doing the same thing in a couple of years.

Steve

Thanks, will buy a quality lock. I'll look for the Schlage brand.

I bought a Dremel Rotary tool about 2 months ago. I haven't used it yet.
Could I use this to drill a hole behind the strikeplate. (I have filler in
there now as I covered it up years ago.) I know I could use a drill or any
chisel type tool. Just looking for an easy way to do it.