I used the play a buggy version, where you can go to Desert Island during the storm. The cashier says you can board as soon as the storm is over, but you can board anytime you have a ticket.
Also there are walkthrough videos on youtube of this verison of the game.
Is it possible to make this GoG version to be the buggy version? Maybe a patch or something? Or is it possible to purchase this buggy version somewhere?

I used to play that (10++ years ago) and I'd like to play that again.

You only need to replace the SCENE.HQR file with the buggy version to be able to do that. You don't need to buy the game again.

I had the buggy version on disc.
I could buy a ferry ticket just fine but when I showed the ferry captain the ticket he just ignored me.
But if I "used" the ticket on the ferry itself, it took me straight to Desert Island and when I was there it was broad daylight and rain at the same time.

There is no non-buggy version of the game. The bug you mention is still in the GOG version (I just tried).

I did notice previously, though, that there are some differences between the game when you run it in Windows and when you run it in DOS (or DOSBox, as the GOG version does). One of the differences is that in DOS, the ferry is not visible during the storm. However, just go to where the entrance of the ferry *should* be and use your ferry ticket, skip the cutscenes (that won't progress because the ferry isn't actually there) and you'll be on rainy Desert Island.