Confining DNA molecules with high throughput and structural integrity is an important challenge in nanochannel-based genomic mapping technology. Here we demonstrate dynamic confinement and linearization of DNA polymers within an embedded nanogroove array with 95% channel occupation. In standard nanofluidic technology, the free energy of confinement experienced by the DNA molecules increases strongly with decreasing device dimensions, leading to a suppression of molecule concentration in nanoconfined spaces. We overcome this limitation by combining "convex lens-induced confinement" (CLiC) geometry with in situ electrophoresis, simultaneously establishing gentle and continuously adjustable nanoconfinement and precise electrokinetic control. Together, these capabilities enable trapping and visualization of extended DNA molecules with high yield over an extended range of conditions. We demonstrate 10-fold increased DNA concentration in a confined region from 10 to 500 nm. Moreover, we develop and validate a predictive model for describing electrokinetically controlled molecule enhancement in continuously varying nanoconfinement. We show that electrophoretic side loading, in continuously varying confinement, not only enhances DNA concentration but also contributes to extend to their full contour length.