This is in all likelihood not a new idea but...
Would it be a halfway decent idea that a mob that takes 21 hours to pop (or more, whatever) can pop and be yellow for say 5 seconds. Something short but long enough if you're watching then you can see it. Then if you perform some action on the mob in that window the server /randoms for you?
The way I see it - the /random done by linkshell leaders is the most civil way but can be interrupted by a rogue claim
Problems:
More people = more chances: But if your linkshell wants it more, maybe you deserve that chance?
Sub problem: Low level mules bumping numbers - could be fixed with a minimum level.