Beautiful piece of myrtle!
You are on the right track with the pattern: Screws, extra wood, glue, Bondo and a lot of sanding!
What caliber is the rifle? The grip area is looking a little thin for anything larger than a 300, might be the camera angle. I reinforce grips on big bores with a section of alloy all thread: Glued into a hole drilled in the grip. Drill the hole from the action area prior to inserting pillars. A 5 to 6 inch length of 3/8" or 1/2" all thread epoxied in the hole will greatly strengthen the grip. I have seen grip areas split from heavy recoil. Can't find alloy all thread, then use a grade 5 or grade 8 bolt with the head cut off.