I ran open cell sponges in a Hagen for quite a while; I saw them working both biologically and mechanically. I would never kill my cycled sponge by putting it in fresh water let alone a detergent!.
Are there other methods of bacteria export besides a skimmer?
Bacteria are a great way to control some nutrients but you need a method to export them, such as a skimmer. If you do not, then the nutrients are still there and as soon as the bacteria die they will release those nutrients back into the water column. Since no filter for our tanks is 100% efficient you should employ several forms of export.
This sums it up nicely I think. You need to be exporting nutrients in balance with adding them (through feeding). I think a skimmer is as close as we get to a required piece of equipment, although clearly there are alternative mechanisms. I have a heavy fish population in my tank, and feed more than is probably wise. I run:
1. ASM G4+ skimmer with a neck swabbie that seems to keep it running efficiently
2. Recently added a waterfall ATS, and it is growing green turf algae gang busters
3. I have designed my sump with a settling chamber form which I siphon detritus once every two weeks as part of my 10% water change (I don't use filters socks, don't like them)
Do you have any details on your sump?

Well, it's nothing particularly fancy, just an initial chamber with a baffle that runs 15" high so there is plenty of height for the particles to settle. Also, I am in the low-sump flow camp - probably run no more than 400 gallons/hr through the 75 gallon sump.
Basically I run most of the drain from my tank through the algal turf scrubber that is over the settling chamber area. There is a 12" 1 1/2" PVC pipe that extends out of the bottom of the scrubber to direct water to the middle of the settling chamber, and gravity takes care of the rest. If I had thought of it before, I would actually have put a bulkhead and ball valve at the bottom of the settling chamber to easily remove the buildup - as it is siphoning the chamber is OK, but a bit awkward. In the photo above, you can sort of see the black/grey buildup that occurs in the bottom.