I would like to know who tries to see the Cross in every verse. Even so, accusing people who try to connect Jesus with every part of the Bible as reading into Scripture is going a bit far. Didn’t Jesus show His disciples everything concerning him in the Scriptures?
And he said to them, “O foolish ones, and slow of heart to believe all that the prophets have spoken! Was it not necessary that the Christ should suffer these things and enter into his glory?” And beginning with Moses and all the Prophets, he interpreted to them in all the Scriptures the things concerning himself. -Luke 24:25-27
Wouldn’t you like to have been in on that conversation? Later on in the same chapter:
Then he said to them, “These are my words that I spoke to you while I was still with you, that everything written about me in the Law of Moses and the Prophets and the Psalms must be fulfilled.” -Luke 24:44
“For if you believed Moses, you would believe me; for he wrote of me.” -John 5:46
It looks like Paul had cross centered living at the heart of what he was doing:
For I decided to know nothing among you except Jesus Christ and him crucified. -1st Corinthans 2:2
You shouldn’t force a theology, and you probably shouldn’t downplay one either.