A general rule in learning my Rebbeim taught me way back when is: when you have a problem based on a Hanacha, throw out the Hanacha!!!
That obviously depends on how strong the hanacha is and where it comes from.
For example, the Aruch Hashulchan (34-36) explains the R’ma 253 in context of “makom mitzvah” which is equivalent to tzorech gadol.
http://hebrewbooks.org/pdfpager.aspx?req=9101&st=&pgnum=47
I found a fascinating B’er Moshe who addresses the refrigerator shaila. Vol.6, 9-11 in ?????? ????????.
He is mattir l’tzorech gadol, and says that in that case, “hakol modim”.
Let me know what you think.