SWIM just gravity filters and washes with methanol, then combines everything (solution goes cloudy as more K2SO4 crashes out, but this doesn't affect the separation) and goes ahead.
Have you tried not filtering the mixture and then extracting with DCM? Simply keep the solids with the DCM, then add a solution of 10% Na2CO3 of equal volume to the DCM extracts (which will contain the solids)... everything should dissolve, and the Na2CO3 helps clean up the epoxide before rearrangement.
Try it, I bet it will work like a charm for you V_L.