You will always have to look for the files yourself because the files are copyrighted material. If a homebrew application could get them for you, it would be considered illegal. Either way, you will have to use the homebrew application Daybreak to update the firmware which comes bundled with Atmosphere.
If you make a backup of your emuMMC with Hekate, then you can restore that in the event the update fails however that is extremely unlikely.
All you do is make your own. These tools have always been available but people are just lazy so they never tried to make their own. You can use this
tool assuming you have Windows.
Do you have a reboot_to_payload.nro file on the root of your SD card? If not on the root, is it anywhere else on your SD card? It sounds like instead of launching hbmenu.nro, its launching reboot_to_payload.nro. If you get rid of that file, it should fix your issue. Don't worry, you can always reboot to a payload by using the Restart function from the Power menu while in CFW.
I'm not sure why you cannot just name drop the game here but I suppose you have your reasons and it won't help me much either unless I've personally played or have experience with the game. In any event, based on the one other user who appears to have had this issue from my search, it
could be a regional thing. The issue was never resolved in that case but it was the conclusion that OP and one other user ended up reaching. This was the
thread in case you were curious.