Is there any chance you might be able to adapt something like this?

In[1]:= Clear[x, y, z];
a = Table[
   x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + 
   x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + 
   x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] - 
   x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + RandomReal[{-5, 5}], {10}, {10}];
b = Table[
   x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + 
    x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + 
    x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] - 
    x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + RandomReal[{-5, 5}], {10}, {10}];
c = Table[
   x^RandomInteger[{0, 3}] y^RandomInt{0, 3}] z^RandomInteger[{0, 3}] + 
    x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + 
    x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] - 
    x^RandomInteger[{0, 3}] y^RandomInteger[{0, 3}] z^RandomInteger[{0, 3}] + RandomReal[{-5, 5}], {10}, {10}];
n[vx_?NumericQ, vy_?NumericQ, vz_?NumericQ] := Module[{na, nb, nc},
   na = a /. {x -> vx, y -> vy, z -> vz};
   nb = b /. {x -> vx, y -> vy, z -> vz};
   nc = c /. {x -> vx, y -> vy, z -> vz};
   Norm[na.nb.nc]];
Timing[NMinimize[n[x, y, z], {x, y, z}, Method -> "RandomSearch"]]

Out[5]= {58.765577, {1395.32, {x -> 0.30773, y -> 0.808193, z -> -1.31719}}}

That forces numeric substitution for each of your matricies individually and then minimizes the norm of the dot in 30-60 seconds. Yours may be somewhat slower because your matricies are apparently far more complicated. We can't tell if this will work for you until you try it. Let yours run for an hour or so and see if it finishes or not.