The neurosurgeon recommended surgery (retrosigmoid), the LINAC radiosurgeon recommended radiosurgery (but only fractionated!), the ENT recommended surgery (translabyrinthine) and the Gamma Knife radiosurgeon recommended ... surgery ... but would do Gamma Knife if I wanted.
Take a look at images of vestibular schwannoma on the web and you can see how much brainstem compression there can be. I've only researched vestibular schwannoma so can't comment on how meningioma would differ.
My facial nerve is stretched enough to go around a 2.5 cm tumor, and there is little deficit.
Brainstem compression can results in ataxia (affecting movement on the opposite side of the body to the AN) and obstructive hydrocephalus. To get throat paralysis, loosing ability to swallow, there would have to be significant pressure on the lower cranial nerves (IX, X and XII).
I would talk to several other doctors.
I'm not a doctor, so check anything I've said independently with several doctors. Also, my research is based on an AN, not meningioma