Srimate Raamnujaye Namaha,
Swamy, thanks for explaining the basis of your question.
Swamy from logical perspective,
One who travels in Triloka does not directly imply that they have restriction to spiritual world.
Though he appears as son of brahma, it does not mean in that each andam , brahma should have same number of children and same names and same type of personalities.
Even if it is the case why should we conclude that all Naradas cannot have access to Vaikunta?
With regard to references:
Narada Muni is the acharya of Vedavyasar as he instructed him to compile Srimad Bhagawatham.
We assume that all our acharyas reach Vaikunta after their service here..so in that angle as well we can very well assume that Narada Muni has access to Vaikunta.
Let me search for more direct references, Krishna willing will share them.. for now please see if this reference helps.(where it is explained that he can travel across material and spiritual worlds)
Another simple angle is , Vaikunta is the place where Lord resides. So In case of Pure devotees like Narada Muni, Lord is fully manifested within the heart.. so a local Vaikunta is already there.