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.
If the material arrived warm and it was lyophilised, test it and proceed on the result.
The relevant detail is that number of stopper piercings matters less than the gauge doing the piercing.
Worth saying: if your arithmetic and someone else's disagree by a factor of ten, one of you has made a unit error.
The practical summary: fine gauge, gentle swirl, diluent down the wall, room temperature before drawing, and check the syringe scale.
edited 3 Mar 2025 by coldbox9 — corrected a unit error in the worked example