STM32H7 with 512MB SDRAM
Can I use a DDR chip on a non-DDR controller?


No.


  Is it crazy to attempt to add 512MB of external SDRAM to a STM32H7?


It's just barely possible, but probably not worth the trouble. The largest SDRAM parts available are 512 MBit (not MByte). They can be configured as 64M x 8. Four of these in parallel can operate as a 64M x 32 = 256 MB memory; two banks of this gives you 512 MB.


  Would perhaps Quad-SPI Flash fit better?


No. Flash isn't appropriate for applications which require memory to be continuously written to.