I was already yo offer my method but every factor you seek or regulation you must adhere to rules out...
"Stuff it under the seat, no case!!!"
I am able to shove my 18 inch barreled Mossberg 500 right under fully loaded if I wish.
I do like them overhead units that fit in your original sunvisor holes... A trigger lock on an empty gun in a case should be legal in the overhead.
Brent