[gsllamdv] Minimum area bananagrams

What is the minimum sized square into which all the Bananagrams tiles may be fit, forming valid words?  (Or Scrabble.)  Or circle.

One could ask rectangle or convex hull but I suspect the answer would be a long thin rectangle.

Could be a good idea for a contest. Break ties by maximizing the density inside the (N-2)-by-(N-2) inner square, then further smaller squares if necessary. Prefer density towards the center, as that can be potentially easier to improve.

A similar metric for circle, decreasing the circle radius to intersect lattice points, probably provides finer-grained tie breaking. Is the center of a minimum disc covering a subset of lattice points guaranteed to lie on a lattice point or half-lattice point? OEIS A057961 and related.