Here's the solution. There's a small code in Project M that makes the stage skip the second part. If you remove that code, the stage won't skip that part anymore. Anyway, if you use the stage as is after removing the code, you'll get lighting issues, cause the Castle Siege in Project M has been edited so the lighting in the transition fits the 3rd stage instead of the 2nd one. You'd need to revert the scenedata settings to those of vBrawl. You'll probably get a decent result by just removing all the files related to the Castle Siege stage from the SD card though.
Now, the how to:
1- Get this file:
http://www.mediafire.com/download/0y2dmm2cwwuqcpa/SiegeRestore.gct
2- Download this tool of mine:
http://forums.kc-mm.com/Gallery/BrawlView.php?Number=20040
Place both files in your codes folder, where 'RSBE01.gct' is. Open the GCT Fusionizer tool, it will ask you for a file. Select the SiegeRestore.gct file.
Once selected, the tool has two buttons, 'refresh' and 'apply'. Press the 'apply' one, and it will ask you what to do next, as the code has been found in your gct. Select the delete option, the code will be removed from the RSBE01.gct file, and you'll be able to play a 3-stage Castle Siege stage.
It's obvious, but don't play that stage on wi-fi once it's changed back to the original number of transforms.