And I would ensure that Y was a poor solution.
How do you ensure people don't think you're not good at your job, if you continually propose poor solutions? Since you're emailing other teams here, they probably(?) don't get to work with you day-to-day to realize you're doing this on purpose.
Also, what's the point of Y being a poor solution? Even if the other team isn't very responsive, can't you always propose your
best attempt at solving it
such that even if they don't respond, you can implement a decent solution?