Has anyone any experience with drawing foundation below brood chambers?

I have a lot to draw and have been placing it above.  The problem comes in 
fall, when some is undrawn or partially drawn and cannot be left above the 
brood chambers because the bees will follow the heat up and cluster there 
and starve.  Don't ask how I know.

Removing undrawn boxes and frames is a nuisance to the beekeeper and a 
disruption to the bees.

On the other hand, if boxes of the new foundation were placed below the 
brood chamber, then it would not interfere with wintering and need not be 
removed in fall.

It is natural for bees to start building at the top of a cavity and extend 
downwards, so this seems to me to be more natural than placing the new boxes 
above, especially in a situation such as mine where no honey is to be 
harvested anyhow.  It would sure save me a lot of work and I could leave the 
foundation on the hives until the bees finish it, even over winter.  The 
extra space below the occupied boxes enhances wintering -- exactly opposite 
of what happens when extra empty space is located above. 

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