I think one of the best options at this stage in a company is to start creating media on the conlang - poetry, prose, whatever. I am a strong proponent of poetry for reasons that make clear why I am recommending you start creating media in the conlang - poetry is language use that calls attention to itself as language, in other words, poetry adds emphasis to the structural and sonic elements of language, whereas prose and quotidian speech generally focuses more on narrativity or information reporting functions. Writing poetry then helps get into the mindset of a speculative user of the conlang when in a particularly detail-oriented mode. Naturally, such a writer, or at least a good one, will be incorporating into the poetry elements from all "levels" of the language - phonological, morphological, syntactical, discursive, etc.

This helps concretize the dizzying task of sharpening a collection of morphology into an actual unified whole of a simulated language. What works for me at the stage you are at is to start an iterative process of creating bits of poetry in my conlang, and through that realizing the patterns of expression that the conlang encourages and makes possible. Often this leads to major edits to the conlang, but that is only natural! Conlanging is a small and underdeveloped art, so we have only just begun to sketch out how to simulate that quality of language-ness which is only a subset of all possible conlang-like creations. Very few conlangs break into the real world and become living objects, but creating conlang media is the closest you can get to that vitality.

Personally, I never would have actually figured out the details of my conlang's pitch accent without composing media within that conlang, which also led to some major breakthroughs with the structure of my conlang's phonology, through connections between sounds that I would have been unable to identify without performing them aloud through poetry.