The Furniture is just enable/disable, just like all house mods.
What I am looking for is how the 'Sawn Wood' is added to the wood pile. Its not a container. Its never added to your inventory. I have found 2 global variables for logs, but changing either does nothing the the count on the wood pile. It has me stumped and I would like to see the dialogue scripts to see what they are doing...
show BYOHHouseLogCount
It shows you the correct amount, but changing it from the console does not update the log pile.
I know you can change BYOHHPAmountLogs which alters how many logs you get with each purchase; although, the dialog still says 20 you will get the modified amount.