Garmin Nuvi here, with lifetime map updates, and I'm very happy with it.
My GPS records trip distance, so it is a second source of distance travelled, but doesn't have an permanent odometer function.
And, yes, you're going to have to get that odometer fixed.
BTW, why isn't the company/department providing a car if you have to drive all over the place (especially into the bush) in the course of work?