I made a rar archive of the layout of my SD card data starting from the root. Currently my only active hack is the project M fox replacing only the default fox color 00, which runs ok in vs mode without any freezing. I keep my other hacks in the textures folder and move them over to the SSBB folder when I want to use them.
https://www.dropbox.com/s/agdfx12nhfqa5p7/Sd%20Card.rar?dl=0

The cd can run subspace emissary without the mods without ever freezing, it's when I load them with riivolution that the problem occurs.  I've beaten subspace a few times before without issue with no mods. The only thing I have on my sd card is the aforementioned project M fox and wolf. This problem has followed me through two different wii consoles and two different brawl discs. I've never actually gotten subspace to work with mods without an eventual freeze up.

So, I think I spoke to soon, the crashes are less but it still happens. Could it be the way I am using Riivulotion? I just post the mod contents in a folder called SSBB and it seems to work. What could I be doing wrong that the game crashes on Subspace Emissarry? Even when I am not playing a modded character, the game can and has froze.

[Post Merge: October 21, 2016, 10:56:43 PM]

So I tried what you suggested, I was able to play through one of the subspace levels about 3/4s of the way before getting a freeze. The textures do load in game properly but someway through the level it'll freeze up.
Post Merge: October 21, 2016, 10:56:43 PMI'll try loading the character hacks on a different sd card when I get the chance, just to ensure my personal SD card isn't incompatible or otherwise.
Post Merge: October 21, 2016, 11:33:37 PMSeems to have been a hardware issue I believe, switching Sd cards has yielded no crashes thus far. Sorry about that!

So, I completely admit I'm not the most savvy when it comes to Brawl hacking, I use Riivulotion to accomplish my model and texture overrides. This generally works for normal battles without an issue (I don't go all the way and edit portraits or stocks.) I use only two hacks, the Project M Fox and the Project M pirate wolf (updates character model and texture of each). Whenever I play a stage with this version of fox the stage will run for a few minutes before freeze and the game makes a screeching noise until I shut off the Wii. What am I doing wrong that is causing the game to do this? Any answers?