since you said you hooked up your xbox to your oled tv playing halo 2. did you use component to hdmi converter to do so since i think tvs nowadays like lg oled don't support component video inputs anymore?
i think ps1 supports 240p but not 360p though. maybe ps1 supports 480i? maybe 448i like 640 x 448i at it maximum resolution but most ps1 games don't run in 448i because of a performance hit i think. ps1 only has 1 mbyte of VRAM and that probably means its not enough to run games in 448i without framerate dropping and or reduced polygons count so that means many games run in either 224p or 240p. probably many games run in 320 x 240p or 320 x 224p, some runs so somewhat higher resolution than that like 512 x 240p but i don't think i encounter a ps1 game runs in 640 x 448i for gameplay though because of a performance hit.
i don't think there are any 360p ps1 games though since there are no tvs that have 360p resolution. ntsc tvs are 480i so that means a ps1 game or a previous and older generation consoles run say a game at 320 x 240p, it upscaled and output it in 720 x 480i resolution for ntsc tvs. i am not sure how they did it but 240p upscaled to 480i looks really good on tube tvs. they probably did some sort of edge enhancements and whatnot to make it looks really good on 480i tvs.
maybe lowest resolution hdmi can support is 480p. since all videogames run in progressive mode, like your metal gear solid game, it probably runs at 320 x 240p, and it upscaled it to 480p on your ps3 before it sends it through hdmi to the tv. compare to analog ntsc tvs, it probably upscaled 240p to 480i and converts the signal from progressive to interlaced before it sends it to ntsc tvs. if a game is 60p like many fighting games are, it converts the 60p to 60i. if a game is 30p, it converts it to 60i by repeating the frame twice but output it in interlaced mode or something like that before it sends it to analog ntsc 480i tvs.
since you will be playing ps1 games on your ps3. you can rest assured that all your ps1 games will always run in true native progressive mode say like 240p upscaled to 480p before it transfer to your 4k tvs via hdmi. that means better motion i think.
added: i have another question, did you guys move to a bigger house yet or you still live at your current house?