I think your idea to "fake" it over the radiator is going to be your best bet.
I've got radiators under almost every window in this house and the only way I can have long drapes is to extend the rods beyond the windows so I do understand your dilema.

I would keep the panels long and deal with it the best you can. I don't think it's a sin to let the panels hang in front of the rad a little.
FW

we had the same thing in our living and dining rooms when i grew up.

all the radiators had cover boxes that looked like window seats-- they were metal but painted to match the walls.

my mom had box valances made for the windows that were wide enough to hang all the drapes.
each side of the window had a fixed panel all the way to the floor. then she had panels made that only came to the bottom of the sill/skimmed across the top of the radiator cover-- these could be opened and closed with a traverse rod. these panels and the fixed panels were the same fabric and were all lined. she also had sheers over just the windows and each window had a pull down shade as well.

in the dining room we had a triple window above a low radiator that was covered as well. we used the radiator for a sideboard. since the windows were so wide mom only had sheers and shades on the windows and fixed panels of drapes on each side with a valance going across the whole thing.

are your radiators covered? a cover makes them more 'managable' when you decorate-- the look like benches or side tables. since you are looking for a formal look, using fixed panels on each side of your radiators would make sense-- above the window the rods should have a treatment that ties everything together--lamberquin, valance, swags, etc. balance the radiator on the one side of your fireplace with a side table or bookcase of the same size.

diggerb