I don't like the idea of modes that can rather easily be duplicated in custom games.
Maybe some additional content would help them feel more like seperate Gamemodes:
・All melee mode
Could be turned into a Gladiator mode where all champions are put into an closed off arena where they have to fight it out.
Alternatively it could be a King of the Hill mode where you have to occupy an altar for extended duration.
・All adc mode
Like the assassins gamemode this should get a different type of objective and changed gameplay.
Considering ADC is the farm-related role it could have a CS counter as victory condition and Black Market Brawler mechanics to make it harder for your enemy to farm.
・One region mode
・Demacia vs Noxus
I feel like an RTS campaign recreation could be a fun idea to recreate a War theme. Both sides would have to hire minions and build structures and upgrade them accordingly. The jungle would hold materials needed for the upgrades. Each side would have some customized units or upgrades.