Bismillah
as salam alykom
Karbala, just before we delve into the other points, in order to let u know who exactly prohibited Mutaa, here is a hadeeth. I understand you take hadeeth, dont you??
حدثنا مالك بن إسماعيل حدثنا ابن عيينة أنه سمع الزهري يقول أخبرني الحسن بن محمد بن علي وأخوه عبد الله بن محمد عن أبيهما أن عليا رضي الله عنه
قال لابن عباس إن النبي صلى الله عليه وسلم نهى عن المتعة وعن لحوم الحمر الأهلية زمن خيبر
It was narrated under the authority of Al Hassan Bin Mohamed Bin Ali and his brother Abdullah Bin Mohamed, that Ali their father may Allah be Pleased with all of them told Ibn Abbass that the Messenger salla Allah a`lyhee wa sallam prohibited Mutaa and the meet of home grown camels (Humur Ahlyah) at the time of Khaybar.
(reorted by Fath el Bari of Saheeh Bukhari)
Insh a Allah I will provide more hadeeth in order to close this gap here.
What is more important is that the Mutaa which was permitted then prohibited is not the format you explained. This is an invention of Shia scholars who actually made it permissible to be concluded while both man and woman standing over the head of (I will verify the name) of one of the Imams (In the Mashhad). We need to accurately identify who is introducing innovations.