I'm making a cake similar to this and not sure if it's all white fondant and then the colored fondant goes over the white.
I think you could do colored fondant over the white, using the draping to cover the over lay.
Seems like the best way to go!
I would do the top tier like you said, all white fondant and then lay the red stripes onto that. But the other tiers I would try to cover 3/4 cake with white fondant and the 1/4 cake with the colored fondant and join the seams where they meet. The drapes would hide any imperfections. Use an X-Acto knife to cut the fondant, so your seams will be neat.
Roll out the white fondant the size to cover the tier, now before you cover the tier, cut out the piece where the colored fondant will go. Use a cake dummy or the cake pan to make a pattern of the size/shape of the area to be covered by the colored fondant. Parchment paper is good for this. Now your seams will be almost flawless. IMHO. HTH
Thanks, I knew I could count CC peeps to help me!