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I am looking for input on a computational efficient way (avaliable in ArcMap/arcpy) to create concave hull bounding boxes that simplifies the geometry without removing any of the original polygon. Basically an "OUTSIDE" option on the simplify tool.

Constraints:
Cannot remove any of the original polygon.
Has to be computationally efficient.
Does not rely on external downloads or scripts (very restricted online access, no administrator priveledges). preferably fills holes of "sufficiently" small size.

Background: In my organisation, we have several hundred datasets of varying complexity an size. We use a spatial query tool that lets users know what datasets are present (intersects) a selected area. For this, we use a simplified coverage polygon for each dataset. This polygon can have a maximum of 50000 vertices, which is quite easily surpased on national datasets, and must be a single object (multipart polygon)

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What I would like is something like this convex hull polygon, but that follows the edges into the convex areas. The grey area is a dissolved grid selection, part of my current experimentation. simplyfing that polygon does make a nice simplified version, but includes a processing chain of "select by location" --> Dissolve --> simplify - I feel this can be a quite cumbersome operation on large datasets with thousands of polygons.

So, before I jump into the rabithole fully, is there a way to produce a concave hull efficiently within ArcMap / ArcPy?

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