OGR shapefile output fails - Error 1 in psSHP->sHooks.fSeek()

When trying to use ogr2ogr to convert to ESRI Shapefile format, I get the following error consistently across different files:

ERROR 1: Error in psSHP->sHooks.FSeek() while writing object to .shp file.

The error shows both from command line (calling the program both through OSGeo4W shell and directly) and QGIS Save As... dialog, irrespectively of the input format (tried OpenFileGDB, GeoJSON and SpatiaLite) or the CRS. I have plenty of disk space and write access to the target folder.

I have come across some bug reports concerning this but they seemed to deal with files larger than 2 GB which is not my case (around 1 MB in GeoJSON). This bug seemed to agree with the case but was closed without conclusion. I also tried a related solution from here but to no avail (QGIS starts normally).

I am using an OSGeo4W Express Desktop Install (default setup) with QGIS 2.16.2 and GDAL 2.1.1 on Windows 7 Enterprise 64bit. I have tried to reinstall the whole bundle multiple times, deleting the leftover folder.

Any ideas how to solve it?