I have just used the plastic ice cream pail and with the barrel at an angle have never had a problem with restricting the water flow.

I have a Traditions break open and I take the barrel off and swab the bore with traditions bore cleaner. Which is probably nothing more than red colored soapy water. I also use a 20 gauge bore brush to scrub out the breech plug threads in the barrel. Be sure you clean the inside of the receiver real well. I use Q tips soaked with the same cleaner and wipe all surfaces down until they no longer show powder residue on them. Then oil the inside and out of everything and you're done. If you have the ported barrel, be sure to use the q tips in the ports.