Standard deviations in a sum of voxels

Hi everyone,
I am modeling a cylindrical reactor, which I have cylindrically meshed into ‘rings’ (cylindrical_mesh.dimension = (36,1,40)). To determine its total local power, I use the 'heating-local' tally, which I want to plot as a function of r, then as a function of z. I got the following graphs:
axial heating div_vol
radial heating div_vol

To get them, I added the tally values on z, or r, respectively (and I divided each value by the total volume of the corresponding area).
I run into a problem when I try to add the uncertainties (+/- std_dev). If I assume that the values of each voxel are independent random variables, then I can calculate the standard deviation of the sum (as was done here), which gives me the following graphs:
axial heating div_vol + sigmas
radial heating div_vol + sigmas

It seems that the uncertainties are really too large, and I don’t know why.

What do you think I can try? is there a way to calculate such a standard deviation directly in openmc?
(I already tried running openmc with more particles, but the difference is not significant. Maybe the assumption of independence of the random variables is wrong, but I don’t know how to do without it, to be honest)

Thanks!