Can you fight May/Brendan again after Delta Episode

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.

You should give Amulet Coin or Luck Incense to your lead Pokemon.

O-Powers can help you, too. Prize Money Power that raises the money gained from a trainer battle, and Bargain Power that decreases the amount of money you have to spend on items.