Non-field-type completions do not interpret infinite fields

Let $(R,<,+)$ be a dense archimedean ordered abelian group, let ${\mathscr{R}}$ be a strongly dependent and noiseless expansion, and let ${\mathscr{N}}$ be a highly saturated elementary extension of ${\mathscr{R}}$. Let ${\mathscr{N}}^{\mathrm{Sh}}$ be the Shelah expansion and ${\mathscr{R}}^{\square}$ the completion structure. Non-field-type completion conjecture. If ${\mathscr{R}}^{\square}$ is not field-type, then ${\mathscr{N}}^{\mathrm{Sh}}$ does not interpret an infinite field. This is a conjectural strengthening of the modular decomposition: the field-type alternative is the only proposed source of an interpreted infinite field in the Shelah expansion.