How will the output of a 12V transformer wall wart differ from that of a 12V SMPS brick?
Dunno about the HAI Electric Strike, but yes, the inrush current may be 2 or 10 or 40 times the hold current. 4.5A rather than 450mA.

Not because the coil current is greater when the plunger is outside the coil, as is the case for AC solenoids.

Rather, because the hold-in current is artificially reduced, either by using a separate hold-in coil, or by switching a current limit into the circuit. You do this to get a good pull-in (what you are not getting) but not wasting power and burning out the coil when the door is left unlocked.

A simple tranformer plug pack had no effective limit to current supply: if you shorted it out for long enough, it burned out. A modern switching power supply does have an inherent current limit: if it doesn't burn out it will still only transfer the rated current.