If you want it to stay at 480p then that preset is not what you want.
The best way to do this is to first manually change the video mode to one of the SD 16:9 presets before you bring in the video you want to modify. So right after you start Shotcut, go to Video Mode > Non-Broadcast and choose between 854x480 NTSC 16:9 or DVD Widescreen NTSC. Experiment between the two to see which is more suited for you.
Then bring in your video 4:3 video and use the Crop: Source filter to eliminate the black bars and make it fit into the aspect ratio you chose. I know you said that you when used this filter it cut off more than you wanted but that could be because you weren’t setting up your project correct. Try again with my suggestion and see how it goes.
Start with the top and bottom parameters then if you need to do the left and right. Make sure to hover the mouse on where the numbers are in the Crop: Source filter and use the middle mouse button to scroll the numbers with more precision.