No, coffee filters would take a very long time.
On first racking it doesn't matter if you carry over a bit of sediment, just try to leave behind as much as you can. Use a syphon tube with a U-bend or a little upturned plastic cup on the end, and as the level's dropping towards the bottom of the DJ, tilt the jar. You really shouldn't be losing any great volume, I would usually expect to top-up around 200ml.