I've come to the conclusion that it's storax from liquidambar orientalis. It sates on the label that it contains Prepared Storax BP. According to a source written in 1990:
"Under the title Prepared Storax the B.P. recognizes only the balsam from the wounded trunk of the L. Orientalis, purified by extraction with alcohol, and containing not less than 30.0 per cent of total balsamic acids, calculated on the basis of the substance dried on a water bath for one hour."
However, I'm still unsure about whether the stale bready note in the dry down is from the storax or from the denatured alcohol. Can anyone with some storax provide the answer? Thanks.