Several coats of linseed WILL make it harder, it's what we use on earthen floors.
Seems like a bad choice for
heaters. The oil is likely to do something funky in the heat.
Something I've used to lock down dusty plasters on a stove is exterior grade white glue. Thin it with
water and paint on a couple-few coats. It'll golden up the color a little and give it a slightly "glazed" look. The exterior grade stuff can be wiped with a damp cloth and seems to slightly resist
coffee stains..