I believe that is about all you can do, although you obviously want to proceed with extreme caution as I’m betting it is looped berber and a little fuzz is better than one of the loop runs coming unraveled. They do make scissors made specifically for cutting carpet called duck billed shears. Good item to have. If you are going to the national conference in Vegas, they are having a carpet repair breakout session that may help with this matter too depending on what they plan on addressing.
In general my experience with wool carpet is that it fuzzes no matter what you do to it. I hate cleaning it as it is expensive carpet, yet often doesn’t seem to last very long (although I’ve cleaned 40 yr old wool carpet that looked 5 yrs old at most).