We just bought a 32k mile 2014 BED this weekend. First google result ends up here. I tried the Hulkamania slam suggestions and failed. I felt like if I body slammed any harder I was going to damage the headrest cushion and I'd be real sorry then.
I have another way to get these headrests down all the way! My way involves a metal file so proceed with caution.
First, the stop pin is on the side opposite of the adjustment button.
You can actually lift the headrest high enough to reveal the notch that catches against the stop pin.
My solution is to file down the 90 degree notch into a 45 degree slope to allow the pin to slide past.
Will try to post some photos here:
Finished photo first. The rear side headrests don't go all the way down. There is a stop pin that prevents the headrest from being completely removed or pushed all the way down. Left headrest is post-modification and pushed all the way down for comparison with the right headrest which is pre-modification.
Lift the headrest high enough to reveal the notch that catches the stop pin preventing the headrest from lowering all the way down. In the photo, this is the bar on the right side, the side opposite the height adjustment button.
Closeup of the notch that catches the stop pin that prevents the headrest from being pushed all the way down.
Partway through the filing. File the perpendicular cut of the notch to become a slope so the stop pin can slip past.
Finished filing. Not as "slopey" as the original, but it shall pass! (with a bit of force)
Trusty metal file and banana for scale.
In case these images don't show up, you might be able to see them by going to imgur here
https://imgur.com/gallery/U1NkTt9 First time posting, so not sure how bad I'll be moderated. Imgur gallery id is U1NkTt9 fwiw.
Safety concerns? I doubt filing down that notch will weaken anything enough to make a difference. Note that this mod only allows all-the-way-down, but still doesn't allow you to remove the headrests all the way out of the car. You're going to have to resort to Popeye-ing that pin into submission for full extraction.
Maybe I simply got lucky with a very strong stop pin? Hopefully this helps someone else who might have an invincible stop pin -- or Olive Oyl arms!