I would first speak with your current Vet and mention the issue re minimising inflammation by giving a NSAID (eg Metacam)
EC is a parasite which, once in the Rabbit's bloodstream, sheds spores. These spores migrate to various places including the central nervous system and the kidneys. The lens of the eyes can also be effected. The spores cause an inflammatory response and the inflammation causes clinical symptoms. So for example should EC spores migrate to the Central Nervous System inflammation there will cause neurological symptoms such as headtilt, loss of balance and hind leg weakness. Once inflammation occurs it causes cellular damage. This damage is often irreversible, hence the need to minimise inflammatory action in the first place.
I am not very good at explaining things so I hope that makes sense. The Metacam would not be to reduce pain but to reduce inflammation. The Vet may say 'your Rabbit is not in pain so Metacam is not necessary'. I would try to have a discussion about the anti-inflammatory action being why it is needed.
If you still feel a lack of confidence with the Vet then you can seek a second opinion. But try talking with the original Vet again first