I don't have a MIST, but it should be possible. The major difference is the usage of altsyncram would need to be converted to SDRAM.
Edit: Ninja'd by Speccery. His post above this answers this.
https://github.com/MiSTer-devel/Main_MiSTer/wiki
I got my DE10-Nano (not DE0-Nano) from Digikey for $130. If for educational purposes, the board is only $99. It's ridiculously cheap (the Cyclone V on it alone costs more than double that).
The add-on boards are optional: SDRAM, IO (VGA, 3.5mm audio, additional SD card, LEDs, switches, optical audio, fan), RTC (real time clock board; not used by many cores, and can be done by the ARM core anyway), and USB-Hub (I just use a use hub cable instead).
There are some sellers of the add-on boards listed here:
http://www.atari-forum.com/viewtopic.php?f=117&t=33613&sid=e5190e475fac31e933cbb2aaf63d9909
I don't need any of these to run the TI-99/4A core. If the full 1MB is wanted, the SDRAM board is needed (The DE10-Nano has about 700KB of altsyncram. I'm currently using 256KB which is 64KB for cart ROM, 64KB for expansion RAM, 64KB for GROM, and 64KB for the rest like yours does; there's also 16KB used for the Video RAM, and possibly more). I think 512KB should be doable, but I haven't tried. I don't have an IO board (using the built-in HDMI instead), but I wish I did as it takes about 30 minutes to compile the version with HDMI on my machine. Also, the free license requires flashing the build directly to the DE10-nano and only works for an hour. If I had an IO board, I could use the lite version which works over VGA, doesn't take nearly as long to compile, and generates an image that can be loaded onto the SD card for any time usage.