1 - You don't need to update the game, just leave it as it is.
2 - About using the modded EBOOT (not the one in the update), you can replace it with the original EBOOT before converting the game to ISO format.
3 - Now the updates, i guess the only way to get official updates is through the PS3 internet connection.
but there is something i haven't tried cuz i don't have it but it may work which is the Multiman, there is an ISO format of Multiman & like i said i never accessed it. now if its the same multiman as in the CFW you should find an Install Pkg option in multiman choose the pkg you wanna install & you'll find it in the XMB to install it.
But don't get your hopes up as may not work, as the developing team said:
The only method currently known of getting homebrew running on those firmwares is if they have the 'discbind' flag. Detailed instructions on how to compile your applications or port existing binary .pkg into a valid homebrew .iso will be released with the user manual.
Now try the Multiman method & reply.