The landmine is the fact that Saber just had a Makiri, who happened to bring up Lancelot to her face when they summoned him last grail war. Sure Shinji did not know what he did but Saber would not see it that way, that what set her off that chapter. Luna came to the rescue there and caused Saber to think that it was a fluke. But if we bring up Gilgamesh up at this time, then she will surely think that Shinji might be doing this on purpose and will lothe him from this point on.
Enemy Saber is a bad idea.