I'll speculate a bit on this.
The problem is that the architects of the scheme (Goodell and Wells among others) have considerable litigation experience and knew at the time that they had to keep their motivations secret, since Brady might sue for defamation. It is unlikely that they would be quite so incautious as to write an email or text that would be clearly incriminating.
I think I'm kind of banking on the NFL being incompetent and also not realizing they were getting themselves into such hot water BEFORE the litigation occurred. Maybe I'm just hoping they were so brazen to not be afraid to send emails or texts with those details prior to Brady appealing and bringing it to court. After all, they did want the appeal transcript to be sealed because they knew it wouldn't look good.
Thank you for your perspective though. It was very helpful.