Abrasive-delivery apparatuses for use in abrasive-jet systems and associated apparatuses, systems, and methods are disclosed. An abrasive-delivery apparatus configured in accordance with a particular embodiment includes a first funnel segment and a second funnel segment downstream from the first funnel segment. The first funnel segment can have a first inlet, a first outlet, and a first interior region extending between the first inlet and the first outlet. Similarly, the second funnel segment can have a second inlet, a second outlet, and a second interior region extending between the second inlet and the second outlet. The first interior region can have a first inward taper toward the first outlet, and the second interior region can have a second inward taper toward the second outlet. The second inward taper can be steeper than the first inward taper when the abrasive-delivery apparatus is vertically oriented.