Beldum Farming/Reset ORAS

The mirage tower is definitely not present in ORAS. The fossils are just laying on the sand in the desert on route 111. An observation that points to this fact.

Also from Bulbapedia -

A Backpacker in Pokémon Black and White 2 makes reference to the tower, saying, "The Mirage Tower in a desert of the Hoenn region has disappeared."

I don't know why you think that beating the Elite Four could change the shiny form of Mesprit. The only shiny locked are Groudon, Kyogre, Rayquaza and Deoxys, as you said.

Anyway it's sure that Mesprit can be found shiny, I think it doesn't matter when you catch it.