We present Single-cell TOtal RNA Miniaturized sequencing (STORM-seq), a full-length single-cell ribo-reduced RNA sequencing protocol, optimized to profile thousands of cells per run. Using off-the-shelf reagents and random hexamer priming, STORM-seq recovers comprehensive RNA profiles from single cells with library complexity approaching that of bulk RNA-seq. STORM-seq identifies thousands of additional coding and non-coding transcripts not detected by existing methods, and recovers clinically relevant structural variants at the single-cell level. We apply STORM-seq to primary human Fallopian tube epithelium (FTE), a complex solid tissue, key to both human reproductive biology and ovarian carcinogenesis. In differentiation trajectory analyses, the improved resolution from STORM-seq reveals intermediate/transitional cell states, and a putative progenitor cell population. The results support a trajectory from a bipotent progenitor population to ciliated and secretory cell types in normal FTE. These findings are consistent across human subjects, sequencing depths, and platforms. Long intergenic non-coding RNAs (lincRNAs) appear as key driver genes in both ciliated and secretory lineage trajectories, underscoring the importance of both coding and non-coding RNA in this tissue. By capturing essentially complete individual cellular transcriptomes, STORM-seq sheds new light on the transcriptional programs that establish cellular state and fate in complex tissues.