Does anyone know an easy method for removing this polymer from the solution? I was thinking something along the lines of setting up a LC column, however don't have the materials on hand to do so.
This is just remotely plausible ... using some sort of stripping column. It is also ridiculously tedious, expensive -- way more so than replacing a reagent, prone to at least some loss, and may even lead to some safety risks.
Replace this reagent. Use it as is, it still precips chloride, right?
Consider -- old silver nitrate solution also yellows in color. You may be facing two separate problems, or no problem at all.