Leaving Japan and Sodai Gomi

If the date of departure back home is some time before the usual sodai gomi collection day, what is the procedure?

Depends on city/ward/town own rules.
Ask to city/ward/town hall or read web again.
Also ask to landlord/andlady or realtor if managed.

Sodai gomi : 粗大ゴミ

ex)
http://www.city.shinjuku.lg.jp/foreign/english/guide/seikatsu/seikatsu...
https://www.tokyo-icc.jp/guide_eng/info/01.html
https://www.city.shibuya.tokyo.jp/eng/living/garbage.html
http://www.city.yokohama.lg.jp/shigen/sub-shimin/dashikata/e.html
http://www.onlinegoods4you.com/waste-disposal-in-japan/
http://www.rainbowfia.or.jp/en/living/07.html
http://sc.city.kawasaki.jp/faq/contents_detail.php?frmId=39932
http://www.tsukubainfo.jp/living/
http://www.nic-nagoya.or.jp/en/e/archives/400