There is no way to currently change a core report to get it to expose custom fields for a component if it does not do it already. It's not unusual an unusual use case to combine creating a custom field with exposing it in a core report. What's needed is to be able to use a hook to add values to $_customGroupExtends. This would also allow extensions to define their own custom fields and add them to a report.

The alterReportVar hook is one place where this functionality could be added https://docs.civicrm.org/dev/en/latest/hooks/hook_civicrm_alterReportVar/. The current three supported varTypes, columns, rows and sql, could be extended by a new one, customFields, or some similar name.

There has been criticism in the past of this hook. IIRC @eileen the concern was especially around how it was not well designed for the sql argument, but I don't recall the details. Perhaps it was that the hook was trying to do too many things and provided too broad a surface.

Rather than further complexifying this hook, an alternative approach would be to create a new one focussed exclusively on the issue of changing custom field exposed by a report. Perhaps it could be call alterReportCustomFields.

So we'd like feedback on

1. Should there be hook support for changing the custom fields exposed by reports?
2. If so, should we change alterReportVar or create a new hook, alterReportCustomFields?