I didn't know where else to ask about this, and FFShrine just came to my mind as a potential place. Last month I remembered a certain movie from when I was a kid or teen, Sonic The Hedgehog: The Movie (I've recently learned it was originally an OVA before being released as Sonic The Hedgehog: The Movie - I'll worry about finding the original OVA later, since I learned there were cut or altered scenes for the "movie" release), so I decided to buy a copy. I live in the U.S., and I use my Playstation 3 as my primary DVD and Blu Ray player, so naturally I have to always buy discs that are region code 1.

When I started looking up the DVD on Amazon or anywhere else, not only did I find out it's been long out of print, but any used copies are selling for around $60.00 and above. I decided just for laughs, to see if it was available on Amazon's U.K. website. I found that it was still available new, and for a lot cheaper, and decided hell with it, I wanted it. I bought it, waited two weeks and it finally arrived.
Before I made this decision, I had done some google searching, and came under the mistake that PS3 players were region-free. I believe that either, ONLY applies to PS3 games, or games and Blu Ray movies, NOT DVD's (I still don't know what it applies to, but I really don't care)

I've since done some more google searching to try and find out if a PS3 can be modified to become permanently region-free, and I can't find any information, other than some random (other websites) forum posts talking about, some people remember some code you could enter on a PS3 using the PS3 BD remote to make the console permanently region-free for DVD's, some others never recalling anything like this, and most information being that Sony has gone above and beyond to ensure the region-coding not only on DVD's over the years, but also with their consoles.

So..... I am wanting to know, is it at all possible to mod a PS3, whether it be a hard-mod or a soft-mod, to make it's player for DVD's permanently region-free? Or, am I better off somehow finding software on my computer, to rip the DVD files, and re-burn the disc as region-free?

And yeah, it matters this much to me. Thank you in advance to anyone who can help me with any of this, and I apologize in advance if this is the wrong place to ask about any of this.

Take this as you want, but having been "in your shoes" a few times through the years, I never modded (nor attempted to mod) the PS3; always preferring to create a fixed copy, instead. I remember using DVD Decrypter for doing it, but honestly, I haven't done that in a while and I could be wrong about the software needed.

EDIT:
Some quick googling brought up that ripping with the aforementioned software will create a "all-region" DVD (Tools/IFO/Region Patch/).

Just use VLC to watch the DVD on your PC. You could go to the trouble of ripping the DVD using something like DVD Decrypter and then re-authoring it, but if all you want to do is watch it, VLC should work. If you have a streaming device attached to your TV, you should be able to cast to the TV. Personally, I ripped all my DVDs (including region 2, which is outside my region) to MKV files using Handbrake. You can even include different language tracks, subtitles, and chapter markers. Each title has to be ripped separately, though (bonus features, etc.). You can set the quality quite high so that they look just as good as the original DVD. You also have to install libdvdcss, which decrypts the DVDs. I don't know what formats play on PS3, but Handbrake can also rip to MP4 (H.264 or H.265).