Software based auto and manual notch filters work pretty well. I've used those between my receivers and computers and the off-air recordings were significantly better than from the unfiltered direct line out. Made a big difference in identifying stations in difficult conditions.
Another listener here has let me "borrow" (virtually speaking) his spare SDR for remote tuning and the auto-notch filter works great for suppressing hets when two stations are very close by, especially when I'm trying to sort out a sideband station while an AM station is on or near the same frequency. I've tried many other web tuners - from conventional receivers like Drake R8's, Icom R-75's and Kenwoods, to black boxes like the ICOM IC-1000 and IC-1500 and Ten Tec RX-320 - and while all work pretty well with signals in the clear none of them can quite match the SDR for really difficult conditions. One notable example is WBCQ on 5110 when there's huge QRM from a ute around 5009 kHz. The SDR's adjustable audio and noise filters, ECSS, etc., work really well in locking onto the AM/USB signal on 5110.
My personal must-have device is a 1990s era Radio Shack "DSP" outboard processor. It works better than it should for a Radio Shack doodad that was intended for mobile use with CB radio. Rather than using the line-out, I place it between the receiver's headphone jack and an external cube speaker. I don't know how it works but it's not just an audio filter, although it does that too. It actually mutes steady heterodynes and suppresses intermittent tones like CW and data to tolerable levels. It's nearly as effective as the comparable filters in the SDR. Unfortunately that Radio Shack DSP is long discontinued and tends to be overpriced on the used market when it appears on ebay - nearly as costly as the used Timewave units which are probably more effective.
The only downside to the Radio Shack DSP is the effect that suppresses heterodynes and data tones also affects music. In particular piano, acoustic guitar and some steady keyboard synth tones sound really odd - as if someone was muting the strings, sorta like using the heel of the hand to mute a guitar at the bridge. In regular audio filter modes the device can't tell the difference between heterodynes and sustained piano, synth or guitar tones, and it treats some short duration musical notes like CW and suppresses those. There's a CW filter mode that doesn't suppress short duration tones or data, but it's unsuitable for listening to any voice or other audio content. So it's a tradeoff between noise reduction and audio fidelity.
Incidentally, I don't believe most of these incidents on the funny bands are deliberate QRM. In many cases the ops simply don't hear each other. If you dabble with enough web tuners scattered around the world it confirms my hunch that propagation is so erratic ops simply don't hear another station on frequency and don't realize they're stepping on each other. Unless they're also checking IRC or the loggings in real time they won't know, and if they're transmitting from remote locations or mobile they probably won't have any way to check IRC and loggings in real time. Most of the QRM I hear between 6800-7000 are government, military, maritime comms and pesques, not other pirate radio ops. Can't do anything about those.