Disc player woes

I decided to buy a refurbished DVD/Blu-Ray player to replace my old DVD player–which will only show widescreen movies letterboxed within a pillarboxed 4:3 frame so that the image is small and surrounded by blank space on all sides–and my hand-me-down Blu-Ray player that stopped responding to its remote a while back. (Buying a replacement remote didn’t help, and the buttons on the front of the player still work but don’t allow selecting menu options, so it can’t play anything that doesn’t autoplay.) Unfortunately, the newer device has the opposite compatibility problem from my old DVD player. When I tried playing my pillarboxed DVD of The Questor Tapes to see how it handled 4:3 media, it squished the entire pillarboxed 16:9 output into a 4:3 frame, so the image was way too narrow. And the other three aspect ratio settings all either stretched the 4:3 image out to 16:9 or lopped off the top and bottom. I tried adjusting the smart TV’s aspect ratio settings to see if they could help, but…