or maybe making shinies limited for each breed could be an option. Like for example there can only be 5 catchable charmander shinies in the entire game then if you want to catch or breed a shiny charmander of your own you have to have the existing one first then release it then start shiny hunting for the charmander again.
I know 5 is a small number but it would make the shiny a lot more precious. They could limit the number of shinies to the number the people already have . For example say that there are 100 shiny chandelure (including pre-evos)already in the server then the max number of shiny chandelures(including pre-evos) that the server can have is set to 100. that way it wont like take away the hardwork the shiny hunters have put in to catch the pokes.
however in the case where pple go offline for years with the shiny poke like 3yrs or more the shiny can be auto confiscated and released into the wild.