Received some new parts for the bike today and it confirmed something I was afraid of for a while;
The VO Porteur bars have a tiny grip area and are not suitable for any kind of regular 22.2mm handlebar grip. These are standard 130mm clamp on grips:
I guess it's time for me to look for other handlebars as I cannot seem to find many, if any clamp-on grips that are shorter than this.