Do you have access to ...

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Do you have access to coconut husks and or activated carbon?  You could try making a coconut fiber and charcoal filter. 

http://www.all4naturalhealth.com/make-your-own-water-filter.html

http://www.solutionsforwater.org/solutions/coconut-fiber-a-low-cost-water-treatment-system-for-rural-areas

https://www.linkedin.com/pulse/20140607105215-105135096-why-coconut-shell-activated-carbon-filters-are-most-preferred-pre-filters-in-the-drinking-water-purification-industry

I have used a hydrocyclone with great success in removing fine particulate material from my well water in North Carolina.  I use one like this: https://www.google.com/?gws_rd=ssl#num=100&tbm=shop&q=irrigation+hydrocyclone+separator

You have a problem with suspended solids though probably and that silt is colloidal in nature and super small.  Some type of coagulant (alum) and flocculant (acrylamide) could be used but I'm sure you don't have access to those on a regular basis for re-supply. 

http://www.flocculants.info/polymer-definitions.html