I would check the pinion gear and its bearing for wear first. The gear should not be jumping out of engagement with the rack. If ythe gear is worn, replace it first.
Rather than drilling and tapping new holes, I would elongate the existing holes in the rack. This can be done with a rat tail file. To properly seat the the cap screws. you will most likely need to elongate the counterbore as well. This is best done on a mill with an end mill. With care, it could be done with a drill press.
To properly set the rack clearance, I would mount the rack with the two end screws and use a shim pack to adjust for the right clearance in the center of travel. Then I would measure the distance from the top of the ways to the bottom of the rack at that point. That will be your dimension for locating the rack. Seat the remaining screws and check for proper position at each screw point. Tighten the screws securely and either enlarge the existing holes for the next size larger roll pins or drill new holes. If enlarging the existing holes, I would place shims above the hole locations to prevent the bias from moving the rack.