You might be able to do this without a laser if the tiles aren’t too small and you’re willing to sacrifice some of the finest details like the buttresses of the buildings. Below is a link to the type of inlay I do on the Nomad. The stems of the bush next to the log, just under the hare, are done with a 0.18 mm mill. (The moon is a bit smaller than a dime.) Nomad precision would probably not be required for this.
Another option would be to use a substrate other than wood where you could use a drag bit (the engraving on my hare was done this way). Some plastics/composites would be excellent for this such as the material used in Hive pieces (rather like Bakelite).