John Mitchell-245523 (5/26/2016)
Yes, you need to reinstall as Standard (or build a new server and install on there) and then restore the databases on it, including the system databases. First, though, check that you're not using any features that are only supported in Enterprise. If, for example, you restore a database with partitioned tables on Standard Edition, you won't be able to recover that database.John
You can check if you are likely to bump into this problem by looking at the dm_db_persisted_sku_features DMV
Thomas Rushton
blog: https://thelonedba.wordpress.com