Alan, lag bolts sound like a very practical solution, especially when the builder says it will work. The conventional repair is to sister in new keel bolts, drilling down into the keel and then crosswise to attch bolts or bend hooks into the bottom of the new bolts, and refilling the holes in the keel with new lead or epoxy. A LOT MORE WORK than installing lag bolts, arguably no better result.
Bear in mind that is you are drilling into a lead keel that makes lead dust, hazmat and toxic to breath. The procedure there is usually to use drilling mud (i.e. grease or lube) so that no dust comes out of the holes are you are working, and a particle mask would be good insurance anyway.
I expect you'll need to rent a large drill to make that job go fast, and simply buy a nice shiny sharp new bit for the holes.