Accepted answer
Add the diluent down the vial wall rather than directly onto the cake. Peptides are surface-active and shear at an air–liquid interface, so a jet of water into a lyophilised puck generates foam, and foam is aggregated protein at the interface, not just air.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle.
On the detail: room temperature before drawing is worth the ten minutes. Cold solution is more viscous, draws slower, and is more likely to pull a bubble past the plunger seal.
Published data on syringe dead space in the context of injection-equipment programmes quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more.
The caveat is that this is not a recommendation to administer anything. Research-use-only material is not approved for human use.
None of this is exotic. It is just the difference between doing it deliberately and doing it approximately.