Anitbody neutralization assays have been quite extensively used in cell biology or biochemistry experiments. You may check if any works in animals have been attempted with anti-TLR antibodies. Since immunotherapies exist and since TLRs are located on surface (before activation and internalization), this neutralization strategy in principle should work. 

There is a chemical (peptide based) inhibitor against MyD88, by Invivogen. But they may take long time to synthesize and the compound was out of stock when I inquired them like a year ago. 

You can ask a chemical synthesis company to make the peptide for you instead, since the sequence is known. 

http://www.invivogen.com/pepinh-myd