Does a dictionary exist that goes from full word -> abbreviation? Many only offer abbreviation -> full word
The baidu baike (http://baike.baidu.com/) often has the abbreviation listed under the main entry. 中华人民共和国国家发展和改革委员会, for example, has 国家发改委.  中华人民共和国国务院办公厅 lists both 国务院办公厅 and 国办.  And yes, 家用电器 points to 家电 as the simpler form, although it is somewhat hidden in the entry.