You should try the Frog Feet, the inventor had the same problem in his bathroom and that's how he came up with the idea.
FROG's FEET
Why FrogsFeet?
We developed FrogsFeet™ suction cups because regular suction cups that we were using on a newly designed bath product kept failing in tests on a presumably smooth surface. Upon closer inspection we discovered that the surface was in fact slightly textured, causing the lip of the cup to lose its seal and therefore the ability to maintain suction. After much development and testing we came up with a suction cup that makes just about every other suction cup obsolete. FrogsFeet™ have a revolutionary active polymer seal around the lip that conforms and bonds to a wide variety of nonporous surfaces, from smooth to highly textured. Combining the principles of suction and adhesion FrogsFeet™ can support more weight and tension by maintaining maximum suction over astonishingly long periods of time. They stay put in temperature extremes because the polymer seal compensates for expansion and contraction. They will not let go or slide in moist or wet environments such as bathrooms because the hermetic seal keeps moisture from penetrating the lip and entering the interior of the cup. This makes them ideal for prolonged outdoor use, in heat and cold, rain and snow. Regular suction cups will fail on all counts.
I imagine a zip tie could be added easily enough for extra security. Put two small holes centered along the bottom front of the holder an inch or so apart and wrap the zip tie(s) through it and around the center part of the valance.
Before this idea I had the plate mounted using long molly bolts going through the lower grill. State law in Texas says it has to be centered and 12" off the ground so there's only one place to put it. Didn't look so great because of the shape of the bumper and since you can only use the bottom holes in the plate it leaned forward.