Good for you to have a good movie collection. I too have a small collection (maybe a 100 or so of the classics) and occasionally I might watch one or two over a month’s period.
I never attached the converter box to my TV, just a VCR and a DVD player.
My hubby, EE by trade, has something that records, like a computer, stores and can burn dvd’s, all on a dvr player. He can add memory, similar to a computer, as needed. It’s total geek heaven. It’s fabulous. The only thing is, they’re stopping production of this type of system, he believes too many are doing what we’re doing. Oh well, he’s purchased 2 more of these systems. I created a monster a couple years ago by suggesting we needed a dvr system and get rid of the the video stuff. VBG