From the OP's initial picture, the factory trim plate/bezel appears larger than the replacement radio. I can see this as a problem, the gaps around the side would be visible and allow the radio to flop and vibrate, definitely a no-no for long term usage, not to mention it would it would look like a total amateur hack job if left as is.
From my perspective, if it were ME, I'd acquire a textured plastic plate (Amazon sells them, I got a sheet to replace the dash panel to install new sport gauges), cut and trim it to fit the original hole. Mounting it may be tricky, requiring removing the entire dash panel to glue or "weld" the plastic together on the backside (with a wood burner or soldering iron, with paper clips or staples as "stiches" to lend structural support).
As far as frame support, the original radio has a threaded stud on the backside that corresponds to a metal tab deeper within the dash to serve as a grounding lead & weight support. It also doubles as an anti-theft deterrent (the head unit won't just slide forward out of the dash easily). It will be up to the installer to provide a metal bracket and additional nut/bolt to bridge the distance. Today's head units are dramatically smaller than the older, old school radios of yesteryear. Some radio manufacturers do provide a metal strap for just this, but not all, and for the ones that do, the strap may not be long enough for the task. Many modern radios are designed for installation into recent cars that already have a rectangular shaped DIN hole, and later model factory units are much smaller than a 50ish year old car radio. Also, most "retro" styled units are made to be drop in replacements into Fords and GMs that came with twin posts mounted OUTSIDE the display, as opposed to Mopar's offset posts.
Modern off-the-shelf radios are compact, feature laden units, many come with a remote control, and dramatically cheaper than customized retro units that require you sending in YOUR original radio for upgrading. That Pioneer radio probably only cost a hundred bucks or so, versus a $300-400 custom job. On the one hand, a retro job will drop in easy peasy, lemon squeezy, look like original equipment, and with the original AM face, be practically theft proof, however it comes at a steep price and may not come near the number of fancy features baked into that cheaper Pioneer unit.
Installing a modern sound system into a classic ride isn't easy. I have seen dozens of examples at car shows where the owner decided to leave the original radio intact and chose to install the newer unit inside the glovebox or built a custom console around it under the dash and/or atop the trans tunnel. That last option can also provide the car with a storage box and cup holders too, something the classic car may not have.
You have options, none of them cheap or easy. Check around online or in the "yellow pages" if they still exist in your area. There are companies and businesses that specialize in just this. If you can find one, ask them for proof of their work, most reputable shops keep photos of their stuff if they're any good at it and proud of their work. Ask around at local car shows and car clubs, check out what they have, ask how they did it and/or who did it. Chrysler did their radios quite differently than other manufacturers back in the day, which presents challenges to today's enthusiast.
Sorry for such a big reply.