Boretech's product description claims that Eliminator does it all. When I use it, I start out with 2 cycles of a carbon remover (Slip 2000 carbon Killer presently) with bronze brushing. The first cycle or 2 of Eliminator generally has a small amount of dark stuff on the patch. I think that starting out with a carbon remover gets that fouling out faster and allows you to tackle the copper sooner. I must say I've never used only Eliminator from the get go.
Your brass jag will work, but the wet patches will turn blue instantly because the Eliminator sucks copper out of the jag. The downside to that is that your dry patches will always be light blue, aka false positive. I've learned to deal with that, but plan on getting some Boretech jags some day.