Writing data to flash memory; a practical solution?

And everything seemed to work fine for small arrays - e.g. with i = 2 and j = 2 or etc. Of course, in the actual application, I want i = 4 and j = 720, which is too big for the SRAM, of course.

Depends on the board of course.
A '1284P with 16K SRAM would not be a problem. Here's one that's Duemilanove/Uno- like, 32 IO, shield compatible. Offboard FTDI, or will take an onboard MIKROE483 FTDI module from Mouser ($11)
$5 for a bare board, build it up as you like
Cross Roads Electronics PL listed here