There is some work published in the UK on maternal mind-mindedness (E. Meins) as an early predictor of socio-cognitive development and obviously the early work of Michael Siegal on deaf children from hearing families.
actually we recently published a paper about a conversation-based training in order to foster theory-of-mind development:
Lecce, S., Bianco, F., Devine, R., Hughes, C., & Banerjee, R. (2014). Promoting theory of mind in middle childhood: A training program. Journal of Experimental Child Psychology, 126, 52-67. doi:10.1016/j.jecp.2014.03.002
In that work you can find a paragraph specifically deserved to the Conversational Approach to ToM development, with a lot of references.
If you are interested in younger children this paper is quite interesting:
Ornaghi, V., Brockmeier, J., & Grazzani, I. (2011). The role of language games in children’s understanding of mental states: A training study. Journal of Cognition and Development, 12, 239–259.
Citing your question, I hope that you can find of some interest the works.
My colleagues and I have also recently published a paper on this topic:
Valentino, K., Nuttall, A. K., Comas, M., McDonnell, C. G., Piper, B., Thomas, T., & Fanuele, S. (2014). Mother-child reminiscing and autobiographical memory specificity among preschool-aged children. Developmental Psychology, 15(4), 1197-1207. doi: 10.1037/a0034912
No not specifically as it would seem to apply more to those with a psychology background and perhaps with an interest in children with special needs. Maybe you have found this already:
My background and interest is more early education / pedagogy with 'mainstream' children - you might find this an interesting start for looking into SST:
I my MPhil i looked at a philosophy for children programme and its effect on the development of metacognition of 4 and 5 year olds. You might want to look at the p4c and teaching thinking literature, i read a lot on the conversation and thinking skills. I am sure there is a lot more on the topic now.