If not, is there a way to write "you were" in a short form?
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No, you're, i.e. you are (present tense) is different from you were (past tense).
There isn't a common shortening, but it only saves a letter or two!
You're is uniquely a contraction of you are, and I'm afraid there is no contraction of you were (at least in proper English, there may be a dialect that uses one).
Contractions are generally flexible enough to transfer to other bases without much confusion:
You can also stack them if you are feeling edgy (and with mixed success):
But other than "'d" there isn't a case for adding extra words that fit the truncated part. Just because "were" matches the syntax for "'re" doesn't mean you can drop it into the contraction:
These sentences just don't parse well due to the same word being used for two different meanings without anything but context to distinguish them. The biggest problem is that the context for each is more or less the same:
The could/would problem is similar:
But the advantage here is that either one gets close to the intended meaning. Switching between "were" and "are" is too drastic of a change and too hard to see without clarification.