I usually use a muslin square folded double and pour it through that first to get the big stuff out then use coffee filters for the small stuff, usually works but if not you can try letting it settle and then gently pouring off the top like you would a bottle conditioned beer.
Sounds like a lot of hard work to me. I don't get whisky at all either, I have been told try this try that etc etc single malts blah blah yet still they all taste like something to clean your brushes with.
I'm fine with Gordon's myself, most others appear to be £10-£20 a bottle more now. Anyway, I prefer my homemade Sloe/Rasperry/Strawberry/Blackcurrant Gin made from Lidl's BogStandard Gin bought in France.