there are different patched MIOS :
cMIOS allows launching gamecube burned disc with the console in gamecube mode.
DIOS MIOS and DIOS MIOS Lite are modified MIOS to run gamecube ISO from SD or USB with the console set in Gamecube mode. it's old and limited. the MIOS itself has a file size limit which was reached.
QUAD Force is also a modified MIOS used to run Triforce Arcade games (based on Gamecube architecture).
Nintendont and Devolution are homebrew run in Wii mode, they don't use MIOS at all so they don't have a size limit, have access to all Wii RAM, and have better compatibility.
I think nodoby knows how nor if you can patch MIOS to access all the RAM.
if you are trying to run a gamecube software, maybe you can try Nintendont. (Devolution requires the original disc, so I guess you can't use that loader with a software only).
if your software is in form of iso file, you can try
Nintendont. follow the guide on first post to learn how to setup.
if it's not an iso, but just a dol, maybe you can try Swiss. I don't know how much RAM it has access to (probably limited), but it runs homebrew in Gamecube mode.
or maybe you can convert your dol to gamecube iso and try with nintendont.
If you really want to patch MIOS for development and technical purpose, then I wish you good luck and please report if you succeed or find anything
I don't know if it is useful, but I tried to make a
Features comparison chart for all gamecube loaders.