It helps to see AF as a "focus assist" rather than auto function. It is still the user that chooses focus with "AF" modes, as you get the direct feedback when you are behind the camera. That's also why you need to set the focus before leaving the camera behind for auto portraits and it doesn't try to auto focus alone (and what if it focus seeks - is the self-timer then a 10+1 to 3 secs self timer?). The photographer is always in the loop to do focus selection, by pointing the camera and half button pressing, focus and recomposing, etc. It is not the camera that "locks on focus before hte timer starts" , it is you who locks the focus on a background far far away.
So this is what you need to do when self portraying - exactly the same as normally. You just have to find something to point the camera at, at the same distance you want to be in. Others suggest you use props, which is fine if you are at home or planning it, but most of these shots tend to be spontaneous, so you need to find something in the scene. if you are going to sit on a bench, use the front of the bench, or the back if you will lean back. Maybe you will stand next to a tree or a pole or a guard post, so use those with "focus and recompose". Your kind of camera tend not to have narrow DOFs so you probably don't even have to worry about that.
So it's really just business as usual. Find and lock focus and then take the photo except for the running part before it snaps.