I have made a little progress on this so thought I would share my solutions to help others out:

If I had the line myReportJob.aggregationTypeSpecified = true; setting aggregationType works. I only found this line in code samples provided by users of this forum. I can't find any reference to it in the documentation? It seems strange to me, why would you bother specifying an aggregationType if you did not want to use it???

The CustomReportJob type lets me include conversion info under customOptions so it looks like switching to that report type will solve that problem. However, if you can check a box to include this info when creating a Keyword Report manually, should you not be able to specify that option for a KeywordReportJob?

I'm still stuck on my main problem - how to just schedule one report to get info for all accounts within My Client Center. This would really minimise our quota usage and according to the docs should be easily done.