Private key 5KJvsngHeMpm884wtkJNzQGaCErckhHJBGFsvd3VyK5qMZXj3hS
Isn't that the "correct horse battery staple" brain wallet?
Yes, and is has MANY unspent dust outputs.
LOL, I'm trying to sweep it too XD
The trick here is to do this:
Have at least 0.01 BTC you can use (the more you have, the better). Send it to the wallet where you are getting tons of dust at.
Every 60 transactions or so (you can do this at as few as you want, but 60 should be fine) send the entire balance to a new address. This will consolidate your dust, and because the total amount of output will be above 0.01 BTC, you can do it without a fee.
You can do this as often as you need and it will allow you to avoid any types of fees. Having more than 0.01 BTC is helpful because it increases your "priority" on the network, but 0.01 is fine as well. Based on my own trials, when I do this with 60 or so transactions and zero fees it will take around 12 hours or so to get confirmed, but that's not an issue since all I am doing is compacting dust anyways.
With how many unspent you have, this may not work as well. The best plan is to utilize this method from the get-go.
Don't worry, I'm used to doing this XD But I heard somewhere that if you're not going to be using your Bitcoins for a while, then you might as well let the dust rest there for a while and wait for the priority to build so that whenever you actually have to use your Bitcoins, you can just consolidate them into one no-fee but high-priority transaction.