phil - the Tubbs bore conditioning system is meant to smooth rough bores and remove minor machining obstacles found in all or most rifle bores. If the bores on your M1 and 03 are dirty, corroded or even pitted, they should be thoroughly cleaned. Most mil-surp rifles should have fairly smooth bores if they have seen any use. And all the various smoothing or lapping processes accomplish is to smooth the bore. If you use one of those lapping procedures when you have corrosion or copper fouling in your bore all the process will accomplish is to drive that stuff further into the rifling, not clean it out.
There are whole bunches of fluids and solutions (liquid) for removing corrosion and copper fouling from rifle bores. Do that first and then you may find you have bright shiny bores that do not require lapping or polishing. Also, some rifles foul up quickly and the accuracy goes right out the barrel, so to speak, when this happens so you may wish to check your bores with a good bore light before and after shooting. If you can see any copper buildup in your bore after a few rounds then you know you have to clean it again and then that bore would a good candidate for lapping or the Tubb's process. HTH. Mikey.