Top contributors for a bounding box

Another option to look at is Whodidit

It has an API that returns changesets per tile, for example:

http://simon04.dev.openstreetmap.org/whodidit/scripts/tiles.php?age=1000&bbox=-111.92834854127,40.685132455819,-111.77749252321,40.740783521057

returning

 { "type" : "FeatureCollection", "features" : [{"type":"Feature","geometry":{"type":"Polygon","coordinates":[[[-111.78,40.68],[-111.77,40.68],[-111.77,40.69],[-111.78,40.69],[-111.78,40.68]]]},"properties":{"changesets":"20478128,16462841","nodes_created":"2","nodes_modified":"0","nodes_deleted":"0"}}, {"type":"Feature","geometry":{"type":"Polygon","coordinates":[[[-111.8,40.68],[-111.79,40.68],[-111.79,40.69],[-111.8,40.69],[-111.8,40.68]]]},"properties":{"changesets":"22954115,22954072,22954020,16712027,16449373,15265638,13183220,12441600,12293424,12293394","nodes_created":"24","nodes_modified":"21","nodes_deleted":"60"}},

etcetera

You can then query the changesets with

http://simon04.dev.openstreetmap.org/whodidit/scripts/changeset.php?id=27348492%2C26248890%2C20361446%2C18741987%2C18442800%2C17280797%2C17182635%2C17064018%2C16424995%2C15966785

Which will return add / modify / delete counts per user for those:

[{"changeset_id":"27348492","change_time":"2014-12-09 04:25:08","comment":"adding detail with bing images and tiger data Keep right not connected roads and bad intersections ","user_id":"567792","user_name":"Natfoot","created_by":"iD 1.6.2","nodes_created":"102","nodes_modified":"15","nodes_deleted":"42","ways_created":"7","ways_modified":"16","ways_deleted":"4","relations_created":"0","relations_modified":"1","relations_deleted":"0","suspicious":0},

etcetera.

Have a closer look at OSM_Mapper by ITO-World ... it has several features, like nshowing most active mappers in a defined bounding box.

not an API (directly, except if you can find an internal interface in the JavaScript source) and not with all that restrictions, but do you know who's around me? Also see nearby users.

This Overpass query will get you a CSV of all the contributors who are still visible in the current map data for a bounding box. Now all you have left to do, is count the number of nodes, ways and relations per contributor.

There might be issues with using other files than history files. If using a current world dump, you will miss a lot of contributors with few changesets. I wrote a bit about that in this post.

If this is an issue, you could use these regularly updated full history dumps. Using the history splitter you can make a full history dump for the bounding box that interests you. The history-renderer imports this into a Postgress database which you could easily use to export the data you need.