I used this kit for the same problem: Qiagen mirnaefsy micro kit. Also i dissected the brain in RNAase free conditions. I wiped the surfaces and utensils with RNAzap and RNAwipes.
I would try homogenizing the tissue directly in the lysis buffer provided with the kit. I am not sure how you homogenize with the Trizol and then switching to the kit procedure. Also, think about the centrifuge rotor. sometimes too big or too small rotor can effect the integrity. Hope this helps
Homogenize in lysis buffer such as 0.1MTris Chloride containing SDS, you can use more volume of lysis buffer. Then extract with TRIzol and re-extract or add more, 0.1 volume additional Chloroform: Isoamyl alcohol to the aqueous-organic phase before centrifugation. You can now use the RNA easy columns to concentrate RNA from aqueous phase. The re-extration n SDS helps to extract the higher lipid content from the tissues