IMHO using a breakdown or 3 piece cleaning rod on a CF is not the best solution. I'd invest some money now and save in the long run, by using a coated 1 piece rod and bore guide. The breakdown kitwill be fine for the shotgun though.

Here is what I'd suggest:
Pick up a decent shotgun cleaning kit
CF
1# -coated 1 piece rod (I personally like Dewey's but their are others)
2# - stoney point bore guide (I assume your 270 is a bolt!!)
3# - .277 bore brush
4# -Tip cleaning jag (I prefer coated or plastic to brass)
5# - Shooters Choice Solvent or similar (this will work fine on both shotgun and CF to get rid of powder/lead,etc)
6# - Dedicated Copper Removing Solvent (Barnes CR10, Sweets 7.62, etc)
7# - Cotton patchs (I make my own out of T-shirts this way I can cut them to the required use for Shotgun, ML or different calibers of CF. You can buy them if you wish -you'll need one for .277 cal and one for gauge of shotgun)
8# - Light Gun Oil (you probably already have this item)

As far as cleaning routines.

On a shotgun I pull the barrel off of my pumps, then run a few saturated patches of solvent down, follow with dry patchs to remove excess and then a patch saturated in light gun oil. I clean/wipe the action, lube, re install the barrel and apply a thin coat to the exterior of the entire gun.

CF's I remove the bolt and replace with stoney point bore guide (this bore guidewill keep the solvents out of your chamber and throat area). I run my powder/lead/etc gun solvent first; saturated patchs, bore brush, dry patchs and repeat if necessary(continue till you acheive clean patchs). Then move to copper removal, the routine is the same (repeat until you stop pulling blue or get clean patchs). For copper removal the manufacturer's instructions for use are on the bottle. I then run a patch of Isopropyl Alcohol down to remove any left solvents. Follow this with a light gun oil of the bore and exterior of the rifle for protection/storage. Prior to firing I run a patch down the bore of my rifled barrel firearms to ensure any excess oil is removed.