I'm not sure of the configuration of supports behind the plastic bumper. Perhaps you should remove it and look.
Removing the bumper on most Hondas is not too difficult. There are a lot of plastic clips of varying lengths (depending on how many layers of plastic they reach through). Usually there are a couple screws on the front wheel arches.
Once the bumper is removed you should look for a mounting area that is more substantial than just plastic.
If you want to remove the "plastic" front end on the 2014, like Carfuff2 said there are many plastic clips. I have instructions for removal if you need them. Also, there are several U-Tube videos showing the removal. Check on subjects like installing a base plate on the 2014. I think ETrailer also has one. https://www.etrailer.com/Base-Plates/Blue-Ox/BX2258.html. The video made it a lot easier, but it was still work. BTW, the inner steel bumper has been removed in this picture.
Here is a picture showing the removed front end on our 5 day old new to us 2014 CR-v Ex_L. I had to hurry up and do it while Sharon was shopping or she would have had a cow!