On my 1976 and 1981 B&S engines �f I recall correctly the cowl retaining screws are 1/4" UNC and the rewind starter retaining screws are 5/16" UNC. It sounds as if your main problem is with the screws holding the rewind starter, which are the larger ones. If someone has forced a self-tapper into one of the threads it probably hasn't done it any favours, and it may not work very well with a proper screw in it. Note that the screws are not all the same length - my rewind starter has at least one long one. Also bear in mind that the engines I'm talking about are 9 cubic inch displacement while yours is 13 cubic inch, so it is possible that yours has different screw sizes from mine - it's best to check.
My solution would probably be to check the screw sizes with a vernier caliper, then buy some long screws, screw them in as far as they will go, mark how much excess thread there is, and shorten them with a hacksaw to the maximum possible length. Of course if you cut them off you have to chamfer them carefully or the burrs on the ends will probably ruin the threads in the aluminium castings when you try to screw them in.
