A great question was posed on the BV Professionals Group on LinkedIn.
Espen Roback and Michael Brown both wrote back to recommend Morningstar. Brown says "you can subscribe to the CEF Module of Morningstar Principia. I believe the annual cost for monthly updates is around $650. It has saved a substantial amount of time for me. You can filter and sort based on many different data points, and the results can be exported directly to excel. It is the best solution I have found for CEF data so far."
Another solution? Joshua Lefcowitz has created his own database by downloading weekly returns from the WSJ--