I have done the coffee filter trick. I poured it into an empty bottle first, took a coffee filter and used a rubber band to attach it to the bottle then turned it upside down and let it trickle out slowly into a clean pot. I actually had three bottles filtering at a time that way. I just propped them up and came back later to check on them.
Having said that, I don't bother with it any more. They only loki I make that has a sediment issue is my Apple Pie and I just tell whoever gets it not to drink the sediments lol. I don't know if I am right or not but I think leaving the sediment in there in that case helps the flavor (it's mostly cinnamon and I think letting that stay in helps).
*rum and loki are amazing inventions*