As you said, Izanagi won't be an option as it is countered with Izanami. And apart from Uchiha Kaenjin, there is no other known Uchiha Kinjutsu which you could attract to the discussion.
I also don't know why you bing up the scenarios of Obito and Rikudo Madara, I thought we are talking about MS Obito and not the one who carries the Rinnegan.
Uchiha and Senju powers allow you to control the Mazou, but you still need the Rinnegan to summon it, hence Madara broke the seal and summoned the statue after awakening the Rinnegan. Hence they needed Nagato for Akatsuki as he can summon the statue. In no word it was said that you can summon the statue by merely possessing Uchiha and Senju powers.
In the end, we can't even tell what Obito did to Madara. He seemingly absorbed some of Madara's Senchakra and obtained this rod. Neither the Soul rip nor Gakido were used against Madara. He rammed his hand into Madara's stomach and ripped off a fragment of the Bijuus themselves, not their mere Chakra. Gakido absorbs Chakra by touching you and don't rips off Bijuu out of you. And Ningendo takes out your Soul, not fractions of Bijuu out of your body.
But again, this is MS Obito. No Rinnegan and only the techniques he displayed in the Manga.