As someone who deals with a lot of emotional switching, I feel you @pinklollipop15 . Mood variation can make it real hard to get a point across. And, it always takes two moods. One to send and the other to receive. If either one is off, the signal suffers and it sucks.
This is why sales-people open with questions that anyone would say agree to. Like "do you like feeling good?" or something. It makes common ground and that makes the rest possible.
Personally, I find telling someone in analysis mode that they're over-analyzing tends to invite whole other levels of analysis. Perhaps a better goal to suggest would be synthesis.
There is a French discussion trick that they use to argue productively (they needed it because the French are very political and love to argue).
It's a three step process.
1. State your view.
2. State you understanding of their view.
3. Propose some form of mutual understanding.
I find it works well, because while people feel weird about over-analysis they tend to forgive it if that analysis is at least partially about them. Not just because of the validation but because synthesis is a beautiful thing.