Phillip,
It was hard to tell one Philip from the Phillip for a moment there, and I thought you were thanking yourself for your introspective insights on leading the cuban breaks..

Glad I paused to take a second look.
I have no specific insight on the leading of the cuban break except to say this. I have always been told that a lead comes from the body. If you have ever played telephone as a child, with two coke cans and a string, you will understand the importance of the 'tautness' of the string in between for the messages to go through. So keep that connection tight and toned, and take small steps (since this is a timed step), and you should be able to lead this figure too. That's my opinion.
Of course, if you dance frequently enough with this woman, you could develop your own routine to aid in the signal of the cuban break. 
To get to your question on convention - to my knowledge, there is none. You will find many standard dancers start their first figure of a dance on their right foot - albeit with a preceding single "prep-step" on the left foot to 1) indicate to the woman that he is ready to go, and 2) to commence the dance from a moving instead of a standing position. Now I am not sure what you mean about starting a swing/jive on the right foot, I have seldom seen people do that (lest it was a description of the woman's figure). Perhaps you mean the prep step? Anyway, the point is this. A good dancer can and will signal the position of his weight to his partner. Once she is on the correct foot, complementary to the one on which he stands, it is just a matter of body language to communicate the beginning of the dance. The remedy to this is to take your partner's hand (or her in your arms, based on the dance of choice); once in position, shift your weight from left to right and back again. She will follow you, if she is a good follower, and you will both be on the "correct" foot and ready to start a dance.
You possibly already know all of this. Good luck and enjoy.
Sri.