I am always reluctant to use any piece of electronic equipment close to its stated maximum unless it is clearly stated to be a continuous rating. For most hobby parts the rated values are the absolute max.
A solenoid is different from a motor because it has nothing other than the coil resistance to limit the current. A motor generates a back-emf when it starts to rotate and that acts against the supply voltage. It is why the stall current of a motor is very much higher than the running current.
You may find it difficult to get a solenoid with a low current and a low voltage that has enough force.
Would a small servo be a suitable alternative for the solenoid?
...R