Here are some cards that support the Monarch Archetype or just Tribute Summoned monsters in general. The Monarchs Awaken is perfect because Monarchs only need their effect upon summoning and are beaters the rest of their stay on the field so they are not bothered by the effect negation and as beaters would appreciate the effect immunity.
Escalation of the Monarchs lets you Tribute Summon during your opponent’s turn for surprise disruption. This also lets Mobius destroy set backrow before they are live. Frost Blast of the Monarchs gives you even more backrow removal if you have a Monarh or a monster with a similar statline on the field.
Vassals were made to be used as tribute fodder for Monarch monsters. Escher the Frost Vassal in particular can be Special Summoned for no cost when your opponent has the backrow for Mobius the Frost Monarch to destroy.