Are there any tested floor-ceiling or roof-ceiling designs that specify a wood joist (2×10, “I”-shaped or parallel chord) that incorporate a wood beam (like an LVL) or steel beam?

No; UL is aware of the IBC requirement “Protection of the primary structural frame other than columns”. To date, a manufacturer has not come to UL to test these materials as an assembly. NFPA 5000, Section 8.6 Horizontal Assemblies, allows the condition.