Today I was teasing a colleague of mine who keeps forgetting things. I said "You forgot because it's Friday today... Well, not that you would not forget any other day". I am not sure if it was correct. Also, would past tense be here, e.g. "not that you would not remember if it was Tuesday"?
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The construction "not that you would know" makes sense in English, and is used in much the same way as your examples. However, making that a negative turns it into something rather less clear — because it's already a negative the "you would know" bit should really remain a positive statement.
I'm not sure what you intended to ask about your second example. Where does the past tense come into that? It might conceivably be
The double negative makes the sentence a bit strained, although it's probably still correct and meaningful if you think about it enough. It would be better to say "not that you would remember if it were Tuesday." Although to be fair, the second half of the sentence appears to contradict the first part, so I may not have grasped the meaning you were trying to convey.