This is interesting to me because I would never have thought of supporting a subject in this way. I have little to offer other than conjecture but maybe it will be useful. My first thought is to engage the subject in thinking of their motivation as a resource able to be tuned. To make them agents of control of their motivation. They need to think of the process like a game in which they are a participant, referee and scorekeeper. What I mean is that they are both subject and object and need to be able to 'step outside themselves' and play the game as if they were actually influencing someone else. They could be taught the stages of motivation as you describe and then self assess their own motivational pattern. What do they value most - least? and once that is known to, in a sense, fool themselves by focussing on the 'best' motivational issue at any one time. The notion of Personal Best is an example of intrinsic motivation. Outside regulation is irrelevant for this and he/she may be able to tap into this at the best of times. When this isn't enough,  then they could write down their life goals and use those. When this doesn't work they could look at pictures of their rivals and so on. The point would be to engage them consciously in controlling their own motivational needs. They should never focus too continuously on lower order extrinsic motivation unless necessary because it has been found to have long term negative consequences, but instead focus on the most 'self' motivated level they can manage. 

Try these

Standage, M., & Ryan, R. M. (2012). Self-determination theory and exercise motivation: Facilitating self-regulatory processes to support and maintain health and well-being. In G. C. Roberts & D. C. Treasure (Eds.), Advances in motivation in sport and exercise (pp. 233-270). Champaign, IL: Human Kinetics.

Ryan, R. M., & Deci, E. L. (2007). Active human nature: Self-determination theory and the promotion and maintenance of sport, exercise, and health. In M. S. Hagger & N. L. D. Chatzisarantis (Eds.), Intrinsic motivation and self-determination in exercise and sport (pp. 1-19). Champaign, IL: Human Kinetics.

Another excellent source is the SDT website, they have a list of research reports in Sports and Exercise.

http://www.selfdeterminationtheory.org/domains/sport-exercise-and-physical-education-domain/

Hi  Jonny,

have you thought about coaching?

Coaching can improve Goal Self-Concordance (GSC), helping the coachee to integrate extrinsic goals while improving goal effort that lead to goal attainment and the coachees satisfaction. The basis for this is a strong coaching relationship based on trust between the coach and the coachee. Furthermore, Basic Psychological Need satisfaction (autonomy, competence and relatedness) can enhance goal internalisation while mediating the relationship between the coaching relationship and GSC.