It sounds like you are naturally predisposed to not liking the cold water. Truthfully, there is no easy way to avoid getting cold. What might be difficult for you is that initial contact with the cold, stream water as it first penetrates your wetsuit. A helpful buffer to that initial shock is to take some water with you---possibly a few bottles, left at ambient temp. When you're ready to get in pour them down your suit. That way you already have water between you and the inside of your suit that is going to insulate you from the much colder, stream water. Not doing that means the cold water that gets in needs to be warmed by your body. 40-50F water is going to rob you of more body heat than 70-80F water. You'll inevitably lose body heat over time and still get cold. Listening to how you describe it, I think you're never able to recover from that first encounter when the water seeps in.
If you don't already have one, invest in a full hood. You lose a ton of heat through your head. For me, that was a huge game changer on how long I could stay in the water.