Does anyone know of a good protocol for the extraction of RNA from an alkaline sludge (pH~10 2.0 M Na+)?

I've tried with the protocol from Smith et al 2007 where they use the Tri-reagent followed by a DNase treatment with the "RNeasy MiniElute Cleanup kit" but once I check the integrity of the DNA with a 1% agarose gel I get a smear in my bands and the 28S and 18S bands are really faint. Once I do Agilent bioanalyzer chip I get lots peaks which I assume are from small fragments of degraded RNA and only very small peaks of the desired RNA.

Any suggestions on how I can improve the yield and on how to get rid of the degraded RNA.