Are there any tricks to making a light-textured "whipped cream cake"?
If the directions say that you should beat your cream and sugar until you have peaks, then whisk in eggs then that may be a possible cause of your results. You've just put loads of air into the cream, then you're supposed to beat eggs into it, which will punch some of the air out. What I would do is beat the eggs separately (I'd not just beat them until mixed but beat them until they start to turn pale, that adds more air), then fold them and the flour into the cream. 

Be careful not to overbeat the cream as well, if you overshoot stiff peaks you'll start to turn it to butter, and then you've lost your lift. I'd stop a bit short of stiff peaks, leave it a bit looser. 

Leaving that much sugar out without reducing the amount of cream would mean that you've got too much liquid in your cake. If you have too much liquid it won't be able to crystallize and the cake, while it will rise, will not be able to hold shape and will collapse. I would compensate by leaving some of the cream out. If you weigh all the dry ingredients you can work out a ratio of dry to wet ingredients (the eggs and cream separately). Then if you weigh the amount of sugar you plan to remove you can work out how much of a percentage of each wet ingredient to take out. Or you could just wing it and use 1 1/4 cups cream and 1 3/4 eggs and see how it goes, that's probably about right anyway.