If his opponent is using Monsters, most likely his last card will be Ozzrel, which can also eat up from your own GY, so that's not as efective. And the good thing about my suggestion - Pitfall trap - is that you DONT need to win R1 - if he can only put one unit on R3, that unit will die nonetheless (assuming he doesnt have artefact removal)Curse of Corruption and/or potentially Xavier to banish his renew targets. (There are cheaper options for graveyard hate but Xavier is neutral.) You could also consider bomb heaver to destroy his summoning circle. Don't overdo it though because Xavier and bomb heaver are not particularly good cards in most matchups. Also, you need to win round 1 and have last say in all of these matches, so play out everything in your hand if you need to and potentially push R2 if you win R1 on even.
Unfortunately these garbage decks are now part of the game (at least until CDPR steps up). Good luck!