I've also gone for the squaddie proof approach and keep it simple:
Ballistol spray which I use for cleaning and oil
3 piece rod and attachments
4 x 2
Grease
I spray a bit of Ballistol down the barrels, then work it through with the phosphor bronze brush and let it sit
wipe down all the metal components with a rag soaked in Ballistol
Run the barrels with the jag fitted and 4 x 2 cloth until clean
Final run through with the wool mop fitted.
Remove the Chokes, clean and lightly grease the threads
Thin layer of grease on the bearing surfaces (hinge pins, sides of the action)
Final wipe over with oiled rag and put away
I'm sure there are loads of 'magic' solutions, potions and tools out there, but I like the regular and simple approach.
Oh and every so often a nice coat of 'Slippery Dicks' wax for the wood work