Internal threading using external G76 tool path (back-tool lathe)

We have been successfully using G76 for external threading on our EmcoTurn 120P lathe for some time. We haven’t yet used it for internal boring or threading. We have an application to make some internal Acme threads in a cylinder. We have a right-handed solid carbide Acme (8 TPI) threading tool. When I run the G76 (set up for internal threading) it is apparent that the machine routine thinks the tool tip is pointing up. It moves in but then moves down (rather than up) to retract.

So with a left-handed tool spinning the spindle in the opposite direction this would work, but we have a right-handed tool we want to use. I am wondering if an external G76 would work? I would need to fix the tool retract at the end of the cycle (it goes directly up rather than coming out of the work), but other than that is something inherently different? See youtube link below where I run an external test tool path.

I could also turn our tool upside down in the holder, but the flat that keeps the tool from spinning is on the wrong side. We could grind a flat on the other side of the tool but would rather not do that unless there is no alternative. Is there some other way to get the orientation correct?

Youtube video of external threading toolpath with internal threading tool:

-Tom