I would say list them because it shows your team's ability to innovate. Besides, if Y doesn't like the one you submitted, they might like the other ones.
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And I would say put a watch on them because their focus on their prime tasks may drop. If you are putting in your 100% where will you get the extra time?
Non core creativity kills startups quicker than lack of focus. Why? Because the core product will be making the money not a creative side product. Lack of focus on the problem kills your ability to make money. Look at from the business point of view (yuck, but thats what will allow future creativity).
Remember we are talking startups here, not established businesses. You simply do not have the time or resources. Now in the longer term you are correct. But make sure you understand each startup is in a fight for survival and it requires a very different mindset.