Very quick Question to those familiar with analog multipliers, specifically AD633
The AD633 always divides by 10V.  It says that at the very beginning of the datasheet, in figure 1.  10V is not the same as 10 without units.

When doing calculations in mV and V (or indeed any other mixture of units: meters and feet; kilos and grams; seconds and hours) you should convert everything into the same units before doing your maths.

So for two 60mV inputs, you have 60mv\$\times\$60mV/10V.  You can re-write that as either 60mV\$\times\$60mV/10000mV=0.36mV or as 0.06V\$\times\$0.06V/10V=0.00036V.  Both of these answers are the same.  So you're probably going to have to change your design a bit.

In fact, when you're used to working with different units, you'll start to notice that they always balance.  Look at the units in the two correct equations above. If you forget about the numbers, and just look at the units on the left hand side, you have mV\$\times\$mV/mV.  Cancel these as you would in algebra, and you have mV, which is the unit on the right hand side.  Similarly, V\$\times\$V/V simplifies to V.  If you look at the original equation though, you have mV\$\times\$mV/V, so your answer is in weird units, so you know something is wrong.  This handy trick is called dimensional analysis.