Vertical Mounting Sub

I'm in the process of upgrading my 18' F250 crewcab stereo system and decided that I'll go with a box under the rear seat rather than behind. This creates several challenges for me. (Small box, shallow mounting depth, speaker size limitation and configuration.) On top of these issues I also need to find a sub that will be mounted vertically. Is there an easy way to determine if a speaker can be operated in the vertical position? How about any possible suggestions for shallow mount 12" speakers that would be ok in .5-.6 cuft box? Im not looking to spend more than $300 per sub. Thank you in advance for any help.

i am an idiot wrote: https://www.foxacoustics.com/ProductDetails.asp?ProductCode=FSD%2D210%2DV%2D17

I've seen that box and was curious what that plate was made of. Also why they wouldn't build the box even all the way across like every other builder. I'm going to build my own which will look something like the JL stealth box.

I found the sticky in Car Audio - Hot Topic for determining if a sub is suitable for vertical config. Unfortunately, I was hoping to find a calculator I can plug the values into for quick reference while shopping.

Fitting a twelve under that seat and not screwing up access for passengers will be a challenge. I second the Fox Acoustic. One in my track and have installed a second in a customers truck. The two JL 10W3s love this box. Using a MMATTS 3000.1 (which I highly recommend) the boxes sound fantastic while leaving the back seat still comfortable. Easy to install, built quite well and fits as it should. The plate is made of a rigid plastic and have not found it to be a weakness. Communications with Fox can be challenging. For the money, this box is hard to overlook.