Ok. So your panel is 320x480 compared to the ILI9341's 240x320. You have 2x the number of pixels to draw.
If you are using IM=7, that is 4-wire SPI and will work with ATmega2560 hardware.
I have written an SPI library for ILI9488 but never published it. (or even tested it)
I have never heard of or seen any other ILI9488 SPI library but it is easy enough to adapt any of the many ILI9341 libraries.
Please post a link to the actual library that you are using.
The theoretical time for filling the 320x480 screen @ SCK=8MHz is 320x480x3 = 460800us i.e. half a second.
If you use an ESP8266, ESP32, ARM, ... you can achieve faster SPI and even use DMA.
As far as I can remember, you can only write 18-bit color pixels on this controller with SPI.
If you could use 16-bit 565 like on parallel, the fillScreen() becomes 0.307 seconds.
I do not own an SPI ILI9488. So this is speculation on my part.
You can run the standard "Adafruit Tests" to see how long your library takes for fillScreen().
It is not possible for me to time your video. But it looks like at least 1.0 second to clear the screen.