I would have responded with the above immediately if my account was working.
I have now fixed my account and made a solution that involves a loop containing some accumulators (hypothetically, a box could cycle through all of them twice, but it would be extremely unlikely) and some more that loop on themselves to achieve an even number of outputs. the big loop is random enough that outputs are evenly dispersed. this is probably the easiest solution, granted that you can get the timing right to avoid collision.