Caching EAV data - XML or NoSQL / MongoDB?
I see only two ways, both of them were mentioned in comments.
First, you can really migrate to document-oriented db like Mongo - this is suitable as alternative to EAV. Since it'll be no JOINs and other logic, it'll be very fast and slightly scaled. (So, perhaps you'll be able to avoid using cache).
Second, you can use specific tool for caching like Redis or Mongo or Memcached to save every query result for some time.
But I want to turn our mind to the future of this system. What is planned loading and scaling? If you want to reduce system load, I think the best way is to migrate to document-oriented db.Or, if you want to have result immediately (cache data for reading) - it can be reached by using caching tool, even [if possible] on network level (for example nginx support memcached out of the box).
So, as usual, you should find balance between one-time and continious costs.