Solution 1:

When subjects are connected with neither/nor, the one closest to the verb controls the agreement. Thus, neither you nor I am. Why? Because lots of English grammar books say so.

Sounds awkward? It does. Lots of other English grammar books agree and so does actual usage. As you can see, there's an actual controversy here. There are workarounds that would please adherents of both viewpoints. The easiest one is probably neither I nor you are, but most of your proposed variations would work.

Of course "*Neither you nor I is" is totally wrong, because is doesn't agree with anything in this phrase.

Solution 2:

As a non-native speaker I don't feel competent for this kind of question. Reading the post and the answers I see this grammar problem really is a grey area. I would tend to accept the solution "am", but was interested what Ngrams says about the use in reality. Astonishingly the most frequently used verb form is "are". Follows "is", and the least frequent use is "am".

So this problem has two aspects, one is what grammars say, and we see that grammars can't solve the problem 100 per cent, except providing a mechanical rule. The other aspect is what writers use in reality.

Google Ngrams