Vladimir,
The results relating saturated real-closed fields and No go back to the following two papers of mine.
“Absolutely Saturated Models,” Fundamenta Mathematicae, 133 (1989), pp. 39-46.
“An Alternative Construction of Conway's Ordered Field No,” Algebra Universalis, 25 (1988), pp. 7-16. Errata, Ibid. 25, p. 233.
Moreover, in the 1988 paper (which was submitted in 1982, but did not appear till 1988!) I also mention in passing that certain kappa-saturated initial subfields of No are isomorphic to the underlying ordered fields in nonstandard models of analysis. Furthermore, in the following two works of mine (working in NBG with global choice), the fact that the full field of surreal numbers is isomorphic to the underlying ordered field in the (up to isomorphism unique) On-saturated hyperreal number system is stated and established, respectively.
“The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small,” in Philosophical Insights into Logic and Mathematics (Abstracts), Université de Nancy 2, Laboratoire de Philosophie et d’Historie des Sciences, Archive Henri Poincaré, Nancy, France, 2002, pp. 41-43.
“The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small”, The Bulletin of Symbolic Logic 18 (1) 2012, pp. 1-45.
Although I was aware of the result for some time before 2002, it was only after an exchange of letters between H.J. Kiesler and myself on the matter in 2002 that led me to put it into print.
By the way, the relation between kappa-saturated real-closed fields and real-closed fields that are kappa-dense (in your sense) goes back to the 1960's and is due to H.J. Kiesler and (to a lesser extent) Simon Kochen.
I hope this helps.