I take it there are no differences in terms of security when using large or small amounts, including 0.001 BTC?
There is a massive difference in security, but most people here wouldn't be laundering enough funds to matter. The DOJ even proved not too long ago that when people are mixing millions of dollars they can track nearly every satoshi. These "mixing" programs aren't made to mix large amounts of funds. They're made to profit from the nickel and dime scammers who think they need to worry about the FBI chasing down their $20 fake gift card sales schemes. That's where the high profit margin is, and that's who their signature campaign members reach with their "scam busting" techniques, which are basically just advertising their signatures to those they want to use their service.