Hi, Ian. Your cracks can probably be very nicely fixed. A pro can use colored epoxy to fill and repair them. And this is one of those jobs where you do not have to feel bad about the cost of using a pro. A good one will have the experience to achieve a good color match and the polishing equipment to make a repair almost undetectable. The cost of the polishing grits and abrasives for you to try to make this a DIY job will probably be more than what he will charge to do the work.
If you can't find a pro that does architectural marble and granite work in your area, the next bet is to check cemetary marker establishments. If they don't do this themselves, they probably know someone who does.