My JCP did that when he first arrived, but it sounds like it was far less extreme. He'd "evacuate" himself and his cloaca would stay out as if he was trying to get more out. It just didn't last nearly as long as yours, his was fairly quick.
My Borneo STP is an absolute sweetheart, so I can't give specific blood/STP advice, but I do have a suggestion.
Once you get her out, keep her out for a while. Right now she's getting what she wants when she is picked up. She acts out and gets put away.
I suggest getting her out, getting passed the messy, flailing, mouth agape part and setting her down next to you on a bed, couch, floor, whatever. Just be sure you can get her there without dropping her if she's flailing a lot.
Once there see if she mellows out while next to you, but not being held. If she begins to associate your scent, mannerisms, etc...with something more than a quick, uncomfortable experience she will learn that you're not a threat. Her behavior is indicative of her being scared. Try to gradually earn her trust through sitting with her, moving her to your lap once comfortable, but not confining her.
I hear a lot of people suggesting "short and sweet" handling sessions to start. I used to as well. But in my more recent experience I've had far more success with longer sessions. I feel as if it allows more trust building time between pick up and put away.
I hope this helps! Let me know if you have any questions.
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