Question on the three extant vinaya

Inspired by this post I remembered a question I had about the three extant vinaya (a subject I am sorely lacking knowledge of since I am not ordained) and whether it would be possible to unite them.

It is my understanding that the three extant vinaya diverged long ago and in fact there were a number of further splinters of vinaya offshoots that are no longer in existence. My question is if it is possible for one person to ordain in all three extant vinaya or are they at this point mutually exclusi

Do the three extant vinaya have contradictory rules or would it be possible for a single person to uphold all three? If it would be possible to uphold all three, then has anyone actually done this in the modern context? If not, why not? What is stopping modern Buddhists from uniting the extant sangha into one united sangha?

Surely this would be for the benefit of the world, no?

PS: If it is not possible for a single person to uphold all three extant vinaya, then is there a single place where all the mutual exclusivity is written down? Maybe this is a way to start to learn about vinaya?

You may or may not find this totally on topic, but there are also cases I believe where monasteries may technically be of a school with a certain vinaya , but which they do not completely uphold due to geographical reasons.

For example, Birken Forest Monastery is part of the Ajahn Chah lineage, but located in mountainous Canada, where it gets very cold and there is a lot of snow. I think this makes following some of the rules in the Vinaya unfeasible (like rules about appropriate footwear and on lighting fires for warmth).

Because “it’s by way of elements that beings come together and unite (dhātusova sattā saṁsandiṁsu samiṁsu) … 'twas ever so in the past and will be forever so in the future.” SN14.15.

Do you think Bhikkhus should be allowed to teach non-Bhikkhus about the Bhikkhu Vinaya (rules of the Sangha) according to your tradition or your understanding about Vinaya?

As someone not ordained I am unaware of any prohibition on ordained sangha teaching non-ordained people the rules which they follow. I took it from @sujato’s link above that any serious student of EBT should study the rules.

Don’t worry. There is no prohibition.