Problem is the gray tile extend past the mantle so only solution I can think of is to buy a couple of flat metal strips like you join 2 boards together with that have 4 holes in them & get some screws to match the holes & screw each of the plates near the top of the mantle(on the back of it) so that 1/2 of the metal is sticking up & you can screw that into the wall above the mantle about where the mantle has the decorative scroll things you have on the wall, then you will need to paint over them so they hardly show & put something on mantle in front of plates so you don't even know they are there when looking at it. That would keep the mantle from tipping over. To help solve the 2nd problem of the gray tile showing on both sides of mantle you could get containers with tall grasses(fake or dried) or tree like spiral things with them both identical & tall it would hardly be noticed as your eye would go to the decoration. Perhaps a couple of sea shells for ends of mantle to match the starfish in pic. or a couple of unusual small rocks would work. Some bottles are very tall & skinny & with grasses in them or those things that curl on ends no one would know anything was amiss. If that wouldn't work for you, you have a small space above the gray tile that you could put some kind of hook & drape something over it to hang down & cover the tile. It does look like that heater is vented to outside otherwise it would be very dangerous. I think that is pipe going into gray tile in center & on outside I hope.

I honestly see no other way but cutting the tiles down around the entire mantel so it sits flush against the wall. You are supposed to attach a piece of lumber to the wall (it is cut out to fit around the chimney frame, large enough to be able to use as a point of attachment of the mantel to the wall and then the center between the chimney frame and the mantel is tiled) and mount the mantel that way.
I only say this because it is the CORRECT way to do it, and will fix the issues. You can still plan to have the hearth extended out further than the mantel, you would just have to chip all the tile off, sand it, and replace it. It is not difficult. We just replaced our terra cotta painted tiles and built a mantel around our chimney earlier this year. It took just a weekend.