Sending the Gladiator Beast to the deck is a cost, So you cant chain to it, but after the cost has been made, you can Chain Royal Oppression to the monster that is being special summoned, then Royal Opression will neagte it. Since Oppression also negates the effect of the card that tried to special summon it, then the effect of the Gladiator Beast that was sent to the deck will be negated, but it wont be destroyed because it is now in the deck
https://www.upperdeckentertainment.com/COMMUNITY/forums/thread/1266110.aspx
Oh and on a side note, the reason that Solemn works on jinzo is not because they were played at the same time. ITs because Jinzo's effect to negate all traps is a Continuous effect which has a spell speed of 2. Solemn Judgment is a counter trap which has a spell speed of 3, it is therefore faster and can be chained to jinzo's summoning