While it doesn't copy mana abilities, there are so many powerful effects you'd want to trigger twice this restriction will hardly matter
The Saga starts by turning one of their noncreature artifacts into a 0/4 Wall, just a little bigger than the Dinosaur token you get the next turn
Blue sometimes also shuffling your hand in as well and then draws you cards
Kess, Dissident Mage or other commanders which can flashback Approach are good because they let you focus entirely on getting copies to the graveyard, instead of having to hold a couple in hand
Dragonhawk, Fate's Tempest Three generic, two red legendary creature Bird Dragon 5/5 Mythic Rare Flying Whenever Dragonhawk enters or attacks, exile the top X cards of your library, where X is the number of creatures you control with power 4 or greater
I think the temptation will be to wait until you have all five quality targets