Add new shard - always best?
Nothing here immediately looks like a Sharding issue. Sharding will have a more significant impact on your Reads than your Writes. There are other areas, for Write performance, I would explore prior to spinning up more resources. There is also a larger topic of how your collection is sharded. You could easily, as per your description, have some documents be updated more than others. You could easily have hotspots in an improperly sharded cluster thus sharding will provide you little performance benefit. 

MongoDB has changed since your question was posted. Circa 2014; you can now better leverage bulk operations. In other words, one request could carry more operations. That itself may already resolve the presumed issues you are referring to and eliminate the need for a middleman. If it does not, then yes you could use your proposed middleman approach. I work on a project that utilizes such a solution to pump much more data into a 3 shard development environment with an eye towards 17 shards. That is mainly due to C# driver inefficiencies.

Prior to a new shard, I would first explore setting your read preference to SecondaryPreferred. This will allow your primary node in each RS to leverage more resources for Write operations. 

One could also argue you should reexamine how your documents are modeled. You may benefit from consolidating some documents if the Read operations tend to query a lot of pseudo-related data across many documents.