You would do well to start with a phosphoric acid primer (google phosphating).
This should give a good key for subsequent coats, as well as being an excellent anti rust agent.
With a little ingenuity you could even apply it to the insides of the tubes, which is where damaging rusting most frequently occurs. (But, of course, you know that!).
Since the BB area is not much prone to chipping, as the top tube would be, I think your touching in plan should work pretty well.
You would do well to start with a phosphoric acid primer (google phosphating).
This should give a good key for subsequent coats, as well as being an excellent anti rust agent.
With a little ingenuity you could even apply it to the insides of the tubes, which is where damaging rusting most frequently occurs. (But, of course, you know that!).
Since the BB area is not much prone to chipping, as the top tube would be, I think your touching in plan should work pretty well.