Could the judgment seat and the cross be connected?
I bet you have no idea how few have picked up on what you have figured out about standing before the judgment seat. It was so refreshing to hear you ask if that could be it. Yep! The judgment seat and the cross are like flip-sides of the same coin as I see it. It's not like there's some Roman looking judgment seat waiting for us where God will figure out what He's going to do with us. It was done in Christ on the cross. Everything revolves around the finished work of Christ. The only difference in the future (from our perspective) is the matter of appearance. We will then be seen exactly as He has already made us in Christ. What we see will eventually match exactly what we are. It doesn't match now, but that doesn't change who and what we are now ... but it sure doesn't look like it or feel like it.
Both Paul and John made reference to things as they WILL be seen for the purpose of making it clear the reality of what is true about us even though we can't see it. The "judgment seat" was alluded to in the two Corinthian letters because those believers had gotten so caught up in making judgments based on the senses of the fleshly mind. His use of the judgment seat was to make the point that you see so well in David's desire to be judged by God rather than man. And as you said, the judgment has already been made so that we can stand CONFIDENT before Him ... and not in INSECURITY as in standing before man's judgment. The Corinthians were also forced to consider that some of their other teachers may have been misleading them. It would become more obvious to them each time they listened to the fleshly wisdom and human motivations being dished out by those impostors. Yep, there were impostors among them purposely trying to mislead. If you read all the way through 2 Corinthians Paul says these "ministers of righteousness" were nothing less than Satan's ministers, aka, ministers of sin. Yikes! Huh? That's why Paul sounded harsh in some of the things he was saying.
Of course, I realize that I have probably stirred up more questions than I answered, but I love doing that anyway!! :)