Neo4j 3.0 ships with the bin / neo4j-admin tool for this purpose.
try bin/neo4j-admin import --mode database --from /path/to/db
see http://neo4j.com/docs/operations-manual/current/deployment/upgrade/#upgrade-instructions
The cypher dump is not useful for a large database, it is intended only for small settings (several thousand nodes) for demonstrations, etc.
FYI: in Neo4j 3.0, the cypher export procedure from APOC is much more suitable for large cypher dumps.
Update
You can also try moving from 2.2 to 2.3 first. For example, using neo4j-shell
add allow_store_upgrade=true
to your neo4j.properties` in 2.3
and then do: bin/neo4j-shell -path /path/to/db -config conf/neo4j.properties -c quit
If finished, that backup of your db is on version 2.3
Then you can use neo4j-admin -import ...
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