Just call G_LoadGame for the new menu SP_PauseLevelSelectDef, like with SP_LevelSelectDef (which used to be the SP pause level select menu too); it's admittedly ugly that the game is essentially reloading from save data within the SP pause level select every time, but that's how it worked before as it turns out.
Also made some cleanup to do with G_InitNew, while attempting to find an alternative fix: reset emeralds and luabanks there instead of in Got_Mapcmd, likewise set saved data from SP save files there instead of P_LoadLevel.