Most active DI boxes have a reasonably high input impedance. I think I was hearing the sort of sound that low-quality piezos provide into low impedance inputs. A Paracoustic I think has an input impedance in the megohms.

I was also plagued with hum on the two acoustic fiddles (the electric-only Bridge fiddle was fine) - as soon as I plugged the fiddles into the jack-to-Cannon adaptors in the stage box hum appeared and a DI box would have given me the opportunity of a ground lift which might have cured the hum.

One of the acoustic fiddlers has his own nasty mic adapter - a little active mic from I think Maplins that he puts (carefully, with padding) into the round bit on one of the F-holes, but it sounds very muddy and feeds back (at about 300 Hz) at the slightest opportunity so I can't use that and at the same time get him up to the same level as other instruments.