Running a Boring Head in reverse, I would expect it to unscrew from the arbor.
Looking vertically upwards, on the end of the spindle, a Vertical Mill running forward rotates in an anti clockwise direction.
Viewed from the toolpost or tailstock, a lathe runs forward in an anti clockwise direction.
So, in both cases, if the tool is mounted perpendicular to the body, (parallel to the axis ) of the Boring Head, it will cut normally if used on either machine.
When the tool is mounted perpendicular to the axis of the Boring Head, to bore a large diameter, the normal tools are not suitable.
For this disposition, it would seem that the solution is to make up a tool holder, with an angled bore for the toolbit, so that the cutting edge is beyond, and below, the end of the holder. Into this angled hole, is fixed a toolbit, probably round, ground to suitable angles to cut when rotated in the forward direction.
In this way when a n existing hole, at the normal maximum of the Boring head, needs to be enlarged, the task can be performed.
Howard