Repair broken capstone - options

I've a decorative stone wall at the front of the property, it's capped with a row of heavy stone caps - each 18" by 30" by 5" thick.

At some stage in the distant past the corner of one has been broken off, and, naturally, it is the one that is immediately obvious. I can't hide it, or swap it, as the caps are all different and have a railing set into them, so I'm hoping to repair it.

The chunk missing is triangular - 5" by 4", and the full thickness.

The stone is a pink/grey sandstone and a very well weathered darker grey.

I'm looking for advice as to the best approach to repair - materials, adhesion etc.

My initial thoughts are to drill into the existing stone and bond in some stainless steel heli-bar strips or similar, and find a grey textured filler to build up into the shape I want, finishing off with a dusting of ground up stone.

Would this work? I'd plan on hacking at the stone at the mating surface with the diamond disk, in order to remove the weathering/pollution, and to key the new material in.

My main concern is ensuring it will be robust, frost proof and weatherproof.

I know it will look different, but I'm trying to make it unobtrusive, and I've been successful with matching colours on old pointing in the past, so I trust my eye for these things.