I'm stuck behind one of the bugs that the 1.05 patch fixes. The patch was released to Steam/other platforms on Friday but still hasn't come to GOG. When can we expect it to arrive?

Looks like the most recent patch arrived today.

But be aware: Galaxy just re-downloads the entire 28 GB package and there's no offline patch file (yet).

You're right, they released another patch today and this causes the entire thing to download yet again.

I'm not sure about this, but I think I've seen people say in similar situations that this is likely a problem on the devs' side. They don't properly tell Galaxy which files need to be updated for the new build, so the program just updates all of them.

I would suggest contacting support and asking them to contact Double Fine and explain to them how to avoid this problem when they push another build. If your internet is slow maybe it's also a good idea to disable auto-updates for the time being (via right click -> Manage installation -> Configure). I realise that this is not a perfect solution since it prevents you from getting further updates, but at least you won't have to go through more days of downloading the newest files every time they release a patch.

Currently downloading the whole 28GB game again also. I've lodged a support ticket, will see what they say.
Amazing game, crappy update system.

GOG support responded that the need to download the full game each update was due to 'technical issues', when queried for more detail they advised that they notified their product team but couldnt promise anything.

So was this fixed?

The game updated today (hadnt had galaxy open for a while) and it was only 1.02GB, so it seems they may have.