(But first, a quick administrative note. If you’re sending me something through the Contact/Ask form and want to include a link, please be aware that it filters out HTML, including links. You’ll need to include the URL explicitly, or I won’t get it.)
1. Does Imperial contract law have anything analogous to the “last shot rule” enumerated here?
The closest analogy would be the Rule of Accord, which in keeping with the general rule of mutual informed consent, holds that unless all parties to a contract are agreeing to the precise same contract, there is no contract. (Any altered terms are, essentially, mere non-binding proposals.) If it turns out that that wasn’t the case after the fact, the contract is annulled, i.e., retroactively never existed in the first place, and unless everyone feels like being reasonable people, involves some untangling of affairs back to the status quo ante.
(This, of course, does permit the so-called “Battle of the Forms” in which both parties repeatedly send slightly tweaked versions of the contract back and forth in order to have the last word. *There*, there’s never been any particular urge to fix the problem with some hack like UCC 2-207, on the grounds that people willing to engage in bizarre irrational-sum games like that pretty much deserve their self-inflicted punishment.)
Avoiding things like this, incidentally, is where the traditional obligator “Thus is our contract written; thus is agreement made.” social ritual comes from. It’s not legally necessary in any way, but it’s a convenient convention to ensure that an accord has actually been reached.
2. Would “The contract I read is not the same as the contract the other party claims I signed” constitute a valid defense for non-performance?
…and so, yes, in a manner of speaking, since if that were to be the case, there isn’t and never was a contract to perform.
Of course, it’s also probably an allegation of fraud…