2003 Pontiac Aztek brakes in rear grinding

The left rear makes a pulsating grinding noise upon stopping, it seems the harder or faster I push the louder it becomes. Took it in for service and the noise came back the same day. I called a parts dealer and he suggested I change the shoes ( I did not yet) the shoes seem to have a good bit of pad left on them. Today I'm going to see if I can just clean the internal parts. Is this a good start? I have had new drums turned and put on with no success with that. I've spent about 100 dollars trying to fix this problem, if the cleaning doesn't help I may just purchase all new shoes and internal parts is this also a good idea. I could not track down any specific 2003 Aztec rear brake problems that resemble what I am experiencing. Thanks and hope to hear for you.