Dess–Martin oxidation work up
It looks like you are not the first to get gummed up by the mono-acetoxy iodinane byproduct of this reaction. A seemingly simple solution is given in this article about converting an alcohol to ketone via DMP:  


  The mono-acetoxy iodinane by-pdt can be converted to easier to remove by-pdts during workup by treatment with aq $\ce{NaOH}$ or $\ce{Na2S2O3}$.  


This is not a procedure I have experience with specifically, so I hope this a do-able solution for your problem as I understand it.  Good luck regardless.