>    One way to numerically approximate the result would be to fill the torus
> with point masses and then sum up their gravity on the tested location.
> If we assume that the torus has even density, filling it up with point
> masses is actually non-trivial.

I would have thought the easiest and trivial way is to just sample the 
3D volume containing the torus in a regular grid pattern.  Kind of like 
creating a volume texture of the torus.  You can then divide the total 
mass by the number of points "inside" to figure the mass of each point 
for use in the calculations.  Just choose a resolution good enough for 
the accuracy you require.

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