haven't try yet, I don't know if RPi 4 can't support 4K video but in the spec its even support dual output 4K monitor, maybe your video player on RPi 4 take a lot usage on CPU or memorry of RPi that make it under perform,
and for your alternative setup to make it clear you don't really need 4K output for your RPi 3 since its just handle a little amount of LEDs, you can rescale to lowest res on USB capture option, so you won't be confused with that high 4K res, but of course you still need splitter or usb capture with loop that support 4K60Hz output since it will connect to your 4K monitor