Dude, I sympathize with you. I spent a month in santiago earlier this year and ran into the same problem. Because santiago does not have the tourist activity that SD or the north coast experiences, you are not likely to find listings of vacation rental properties that would suit your purpose. In addition, a lot of property owners in santiago don't like to rent their properties because they have problems with squatters (it can take up to two years to lawfully evict one from your property).
Your best bet would be to contact someone that you know in santiago and get them to locate a short-term rental for you. However, I assume that you had such friends there, you would have contacted them by now.
I eventually had to rely upon the school where I was taking spanish classes to find a place for me (I did not want a homestay with a family). Fortunately, the owners of the school have on-going arrangements with a few property owners. I believe that they will help you out even if you do not take classes at the school.
Now that I think about it, they list rates on their website for those who want to rent an apartment, but don't want to take classes. If you would like to contact them, their website address is American Language Partnership International. Evan, the guy who handles housing and homestays, is a native new yorker that has been living there for some years now. Even if he can't help you, I'm sure that he won't mind steering you in the right direction.