Pour copper area inside cutout Altium 19
I see you've found an alternative solution, but I'll still answer the question you asked in case it's useful for future readers.


  I have tried making a cutout then drawing a copper pour within that, but the copper pour doesn't work, though the cutout does.


You don't need to make a cut-out.

Just put the GND polygon inside the power polygon. Then, in the polygon manager, adjust the pour order so that the GND polygon is poured first. Then when the power polygon is poured, it will flow around the GND polygon, respecting your clearance rules as it pours.

It's also possible to just use the power plane as a reference for your transmission line. The main consideration is just to make sure there is good AC coupling (bypassing) between the power plane and ground planes, particularly near the two ends of your transmission lines.