Wonder if stick on Velcro would work. It peels off easily if you don’t get the expensive type. Stick on to device and seat. Maybe keep the tray table half folded in case it dropped. Try it at home first.  

How about putting it in a suitably-sized ziplock bag - then tape the top of the bag to the seat-back with duct tape or masking tape and let it hang free. You'd be looking through the plastic but probably wouldn't be too bad. Might be affected by whether you're using any cables with it - but you could make holes to run cable/s through.

Edit: Just saw tablet is 14" - not sure if ziplocks come that big. However I guess it doesn't need to be a ziplock at all - any clear plastic bag could do.

On domestic flights, where the pocket for the in-flight magazine etc is above the tray, I fold my folio-style case back on itself and "hang" it from there - makes a perfect eye-level screen. 
Not sure what the solution is for seats that are not constructed that way, other than propping it up somehow. 

Handsomedan:

 

On domestic flights, where the pocket for the in-flight magazine etc is above the tray, I fold my folio-style case back on itself and "hang" it from there - makes a perfect eye-level screen. 
Not sure what the solution is for seats that are not constructed that way, other than propping it up somehow. 

 

I have done something very similar on many different international flights. The sectional folding top cover flap of my iPad folio case is able to slot into a part of the top of the seat in front and hangs from there. Sometimes that flap is able to slot in behind the IFE screen  - but hard to generalize about this.

Handsomedan:

 

On domestic flights, where the pocket for the in-flight magazine etc is above the tray, I fold my folio-style case back on itself and "hang" it from there - makes a perfect eye-level screen. 
Not sure what the solution is for seats that are not constructed that way, other than propping it up somehow. 

 

Ditto, you should be able to hang a folio case in the "magazine slot" 

The only concern could be width, but a domestic seat is described as being 17 inches wide, and the head taper isn't to severe, so 14 inches should fit  .. I'm Flying in the weekend so could confirm the dimension of the gap if you like... 

As for International, it all depends on the seat class..

I have a couple of different sizes if these that I have used on various aircraft seats to hold tablets 

https://www.aliexpress.com/item/1005004891591996.html

noroad:

 

I have a couple of different sizes if these that I have used on various aircraft seats to hold tablets 

 

 

 

https://www.aliexpress.com/item/1005004891591996.html

 

https://www.aliexpress.com/item/1005002265232963.html