My first guess is that the suspended material is due to the oats and not the chestnuts. The chestnut batch I brewed came out clearer than my extract only batches, and that was not because I did a great job. I just steeped with amylase and pectinase as directed by the supplier recipe: http://www.chestnuttrails.com/pages/chestnut-beer
I got no paste at all. The roasted and flaked chestnuts yielded a deep brown clear wart which I boosted with corn sugar and small amount of LME.
I am no expert, but it looks like your mashing temperature is a little high. I think amylase needs the temperature to be in the 145 to 158F and it starts to have trouble over 160F. In the link above, they have their strike water above 160F but the chestnuts bring it down quickly to the mid to low 150's where it needs to be.
The chestnuts are expensive, no doubt. I don't like the taste they give, but others really like it including my wife. I would not abandon them unless you establish that you don't care for them. If you like the flavor, you can always use them in small quantities to add some flavor.