So your curtains are going to have a 6" puddle? NO NO NO. How hot does that register get...if it's going to scorch/ be a fire hazard the you cannot hang curtains in front of it. If that is not an issue the hem should just skim the floor. Given the register and everyone KNOWING why they would be short I may just skim the top of the register and not worry about them being 'high waters'. In this case for sure hang rod just above the window casings...up against the ceiling would emphasize the high waters. There are times when function is just going to win. If it were MINE the couch would be backed to that window with short curtains where no one could see the hem to know.

If they're electric, they're a fire hazard. If hot water, not, no matter how hot it gets.

However, this set up is ideal for shades or blinds, whichever kind you prefer. Curtains not only should be floor length, but much fuller for a window as wide as that.

They are gas baseboard diffusers. I’m not sure if curtains will be a good option for that window. Do you think something like a Roman shade would be a better option? I definitely do not like the idea of having to spend money on curtains that do not fit the window properly because of a heat vent. I definitely prefer my curtains to be floor length. Thank you for your feedback. :)

Yes, I think Romans would be a better option. I would get three, if possible.