Thanks for all of your help thus far.

I know in the rule book it says there are special ability cards that can be played to interrupt the "come into play" attribute, but doesn't say which ones do that.

Looking through the deck the only one that jumps out at me is Moving Search which, among other things, can prevent the "come into play" attribute of traps only. So during the dungeon draw I would play this crawler card to stop the come into play from happening immeditately, then continue the dungeon draw correct?

Are there other ways to prevent it? Is there a way to stop it from triggering with an event card? What other cards are handy for stopping "come into play"?

That's the only one right now (that I can think of as well), it's a game mechanic that creates dangerous amounts of issues with timing, so we didn't delve to deeply or greedily with it.

Also, just to point out, this can be done retroactively. Moving Search does not need to be played when the "come in to play" card hits the table, it can be played during the respond step to undo what was done.