Is the burlap treated with anything, or is it saturated with coffee oils? I wonder if an intermediate use would be good before composting. Mulch, for example, or spread out on unpaved ground on high-traffic areas or walkways (I look for things to keep weeds down on the pathways in my garden but it isn't the same as what I mulch my plants with).
What does shredded burlap look like? Is it stringy (as in a tripping hazard) or small swatches or is it a fuzzy clump of fibre?
Silver Creek Materials in Fort Worth has some unusual mixes of stuff in their compost (or they used to - I haven't heard much about their output lately - they may be doing more industrial than consumer work now, but that is just a guess).
Silver Creek Materials
2251 Silver Creek Road
Ft. Worth, TX 76108