Hi Belgand,
I'm not sure that your problem is solely the 1070...
the only time I had video problems with mine wires were the guilty party...
I do not have a playstation...but I do have a gamecube hooked in composite and component to my 1070...I also do not have the zelda special edition you mention...but I do have two Zelda games for the gamecube...''Wind waker'' and ''Ocarina of time Master Quest''...and as far as I know neither...or any other game on the gamecube for that matter, have given me (I should say my son ) any problems except the obvious limitations...
( I personnaly find the video quality of the gamecube questionable on large displays even with a progressive signal)...
All this to say...maybe your problem is WIRE related...
or
Have you done the upgraded firmware ''thingy''
on your 1070 ?
hopefully you'll find the guilty party soon...
Good luck !