To be exact about it, the switch to a low-dead-space syringe nearly doubles your usable vial, which is better than switching suppliers if you are looking for cost savings.
Dead space quantified: a fixed-needle insulin syringe holds roughly 3 to 5 µL in the hub and needle after the plunger bottoms out. A luer-lock syringe with a detachable needle holds 35 to 100 µL depending on the hub design.
Corollary that follows immediately: changing needle gauge or length barely changes your losses.
Syringe residual volume has been measured properly, mainly in the infection-control literature, with a median residual of about 84 µL for a conventional 1 mL syringe with a detachable needle and roughly 2 µL for a fixed-needle low-dead-space design.
One qualification: the dead space does not affect the dose accuracy if the hub was full of solution at the start of the draw.
The switch nearly doubles your vial, which is better than most other optimisations combined.