Hi,
I deal with this quite a bit. A high quality skull rad...maybe a MRI....should be part of this diagnosis. While it is possible for an upper root to invade the "sinus" (rabbits don't really have a sinus but it helps me and others understand the area if we use a familiar term), it is much more likely that an overgrown molar from the lower arcade is the invading member. A rad will possibly show an impaction of molar roots. It is common in older rabbits as their teeth start to loosen up a bit...which is an advantage when extracting them.
I personally feel that a little more aggressive treatment...especially looking for and treating any possible infection....would be in order I would also suspect that at least a moderate level analgesic would be proper since these conditions are painful. A modified husbandry protocol including feeding of softer food (pellet slurry or greens) and possibly fluid therapy would also help. A culture should be performed to see exactly what pathogen is causing the infection. I would hope the vet would suggest this. We are seeing an increasing number of bacteria here in the US...particularly pasteurella and pseudomonas...that are becoming resistant to some of the commonly used antibiotics. Some of the old school vets still believe in "shotgunning"...which is to give a particular antibiotic without complete diagnosis (a guess). This leads to bacteria that is much more difficult to control. Another reason to properly and quickly diagnose and treat this condition is the possibility of developing a head/jaw abscess which brings on an entirely new world of problems.
I also share your concern regarding the prognosis of surgery. In the hands of a skilled rabbit vet, anesthesia concerns are not as high as they were only a couple of years ago. We routinely use injectable anesthesia now with exellent results since the sedation injection can be reversed by another injection. There is also a newer gas called Sevoflourane that is awesome. It is great with a very quick rebound after recovery. Based on the info provided, I think the risks are outweighed by the overall health benefit of getting a chronic problem corrected.
I would also suggest reviewing this rabbit's husbandry protocols. Maybe get that weight down. An overweight bunny is subject to all sorts of health issues. And bringing weight off a plump rabbit brings it's own challenges due to the way the rabbit's liver metabolizes fat.
We have had numerous dental extraction performed. Short term, it is a difficult surgery. I would count on about 3 days of intensive treatment to get the rabbit thru after surgery. Long term, it is the best thing we did for our buns with dental issues. They are healthier as they eat better. And they don't encounter the pain and stress of repeated clippings/trimmings.
Randy