Seems you found your answer but check out the whole Macross series for more mecha alien fights overlaid to JPOP empowering the fighters

Trigun

How no one has recommended the Macross series is beyond me. It’s not mech vs. mech, but mech vs. alien.

I like Macross: Frontier most, but I’d probably just go through them in order.

Legend of the Galactic Heroes is pretty good too, although it’s less mecha and more strategy.