Searching for 480 is not likely to get you anywhere fast.
The PS1 is noted for having an odd approach to graphics compared to other 3d systems, though if your goal is just to downscale some menus it is a reasonable hack to want to do and should not pose too many problems. I don't know what will be done here but you may find the handling code shuffles things down so many pixels and halving that (or halving + accounting for interlacing) causes problems with the display. Should still function (outside of lightgun games it is not like it cares what is showing) but may be off the screen.http://www.raphnet.net/electronique/psx_adaptor/Playstation.txt
Do a page search for "The GPU is the unit responsible" for the video section start and "·Display area in frame buffer" for more on what you want.
Personally if it is was just for two games and I really wanted hardware I would delight one of the charity shops here and relieve them of one of their many CRT screens but this works too. I don't know if there is anything better than the framemeister out there these days -- every time I go looking it seems like more expensive and about as good as the VGA boxes of years past.
When you say menu are you thinking title screen or 13:37 of https://www.youtube.com/watch?v=yLCLA2uooeo
? For the latter it appears you are spared a single background and that looks like it is drawn up from individual elements which is nice.