Linked Bayes Boxes

(You might think that this is more a more appropriate question for MathEd, but they tell me that it's more appropriate here, so go figure...)

I'm trying to use linked Bayes Boxes in a spreadsheet to model sequential Bayes. Take the following problem (apologies to those of you who actually know Minecraft! :-)

p(night|creeper) = p(night)*p(creeper|night)/p(creeper) 
p(zombie|night) = p(zombie)*p(night|zombie)/p(night)

Separately these are very easy to model. But I want to combine them to get p(zombie|creeper). I could, of course, just build a separate Bayes box for this, but what I want to do it to figure out how to link the posteriors (output) of the first box into the priors (input) of the second. That is, to get something like:

p(zombie|p(night|creeper)) = p(zombie)*p(p(night|creeper)|zombie)/p(p(night|creeper))

Here's what I have built. Is the correct way to link these?

Where C8 and C9 are just F3 (that is, p(Night|Creeper) multiplied by the same p(Creeper|Tod) as above (i.e., C3 and C4) ... (That these probabilities are the same is coincidental, and slightly confusing.)

But there's something unsettling about computing p(p(n|c)|Z) (C89) by merely multiplying in F3. Am I doing something wrong here, and how would I do it correctly? Maybe I need to go to a Bayes Net, but I'm hoping not because I'm trying to teach this to a 7th grader, and we're pretty far down the road with Bayes Boxes. Maybe that was a mistake and I just have to byte the bullet and switch into full Bayes Net formalism.

Thanks in advance for your guidance.