Personally I'd try a heat gun first, I've got a slightly different version of this Steinel where you can dial in the temperature on the back LED. Most 3D filaments should melt between 130 F - 240 F. If I remember correctly, they should have a glass-transition temperature, where the plastic start curling and then they have a melting temp. Somewhere between the to should be perfect. We used to flame polish acrylic back in the shop, the rough saw cut edges were exposed to an open flame which makes them nice and shiny, I don't think that would work with lower melting temp plastics.
I was trying to find something cool to print outside of the multiboard wall and shelves project that's taking some time to do and found a Lightbox Generator on Makerworld.com. This one is fun, I made this box, it's about 20 cm x 20 cm x 5 cm (8" x 8") and it's made kind of translucent so I can put LEDs on the inside, I just don't have any yet. The front cover is removeable once the lights are installed it will be easy to change batteries or bulbs. The photo is picking up white glare from my light, that's why there's white specs. I got the drawing from one of the newspaper ads I posted, cleaned up some of the writing and newspaper artifacts. Now it's time for a Walkman!
Still messing around, I've always loved signs so this is a lot of fun for me. I'm moving stuff around for my office display so I don't have a good photo area right now. The National Logo turned out ok, after some research I need to add more cleaning time to the filiment so it doesn't get the white-washed effect. The Walkman was from an ad that had more detail but I ran it through a free online conversion tool, this was the most delicate version, the other version had chunky black lines that might have been ok but the Sony and Walkman Words were hard to read. The box can open with either a thick or thin top, I went thin thinking the lights would be mounted in the back. The right box shows the thickness, around 1-3/4." The black edge can be changed to any color but I like the border. I was thinking about just making covers but I haven't found a way to pick the dimensions yet in the program, they're coming out similar but not the same.