tl;dr: I've made a patch which will take the GOG version up to Steam's Version 1.2 Beta.

In the worry that a GOG patch may not arrive any time soon, as has often been the case with past Kiseki games (although we have been promised by the weekend - that may be for 1.1 though, I assume it's 1.2 but we do not know exactly), I've taken it upon myself to provide you with an unofficial care package to bump the GOG version of the game to the current Beta Steam version of the game.

This will allow us GOG users may enjoy the current enhancements of the Steam version without having to wait any longer for the patch to officially arrive. It should be noted that this is only possible thanks to the DRM-free nature of the Steam-GOG unified executable, you should really thank Durante and the other developers at or affiliated with XSEED and Falcom instead for making this possible.

The patch comes in the form of a "delta", it contains all of the differences in files between the current Steam version and the current GOG version, thus directly patches the game to become identical to the Steam version. It was generated using a C# utility which I wrote in the space of around 20 minutes with a help of a friend owning the Steam version.

WHILE THE RESULT SHOULD BE IDENTICAL TO THE OFFICIAL STEAM VERSION, PLEASE DO NOT SUBMIT ANY BUG REPORTS RUNNING THIS. RESPECT THE DEVELOPERS AND DO NOT CAUSE THEM ADDITIONAL HASSLE. THIS IS NOT AN OFFICIAL SOLUTION/PATCH, PLEASE DO NOT REGARD IT AS SUCH, IT HAS BEEN TESTED, IT PASSED ALL TESTS, GAME SHOULD BE IDENTICAL TO STEAM BUT PLEASE STILL DO HEED TO THIS WARNING, I DO NOT WANT TO BE A DIRECT CAUSE OF ADDITIONAL DEVELOPER HASSLE.

INSTRUCTIONS AND LINKS AT THE END OF THIS POST

The Extra Note
I apologize to the developers for being such a deliquent, but I do not wish for the same situation to repeat again as with Trails in The Sky SC on GOG, once unmaintained for nearly a year with a set of cumulative updates arriving months later. Currently as of right now [strike]last updated 8 months ago[/strike] (I take that back, it's just over three, seems the base download got updated instead) despite Steam receiving a good few patches since (as not only evidenced by the shining new features such as the DirectX 9 API support but 30 manifest changes showing that plenty has surely happened since).

I understand regarding the pains of maintaining multiple branches for each executable as it has been the case before, but even now, it's been a good few days and the unified executable has not been pushed to SC on GOG, that kind of pains me, 3rd and FC on Steam always get plenty of nifty upgrades and yet it takes literally forever to ship them on GOG, sometimes lengths beyond acceptable.

If possible, I wish at least that Sara in the case of SC and other Sky titles on GOG would push to the Beta channels (if it were to be a faster/alternative/viable option) if pushing directly is not seen as a viable option. I know of the pains of not having the equivalent of live immediate deployment (SteamPipe) available on GOG and the whole burden of the validation process of each update but I do wish for there to be an alternative for faster update deployment, even direct deltas like this one or self updater powered by own web hosts. Stability is not a factor as GOG allows the user to freely choose/download the game version to play, unlike Steam where that is only something that you can force through the Steam console if you know the application ID, depot ID and manifest ID (nowadays made easy with SteamDB).

Instructions
Download the latest GOG patch at the time of posting (1.0.6421.30108) and extract the contents of the 7zip LZMA2 compressed archive into the game folder, done.

Alternatively: Using the Delta Generator
The Delta Generator allows you to create "Care Packages" (like this one) for GOG users and is a tool I whipped up in around 10-20 minutes in somewhat of a rush. It creates a delta/folder of changed files based off of the difference between two versions of the game and guides you through the process.

Basically you get a friend with the Steam version to downgrade his game to X version, the tool will evaluate all of the files and then instruct the user to upgrade or change to Y version, following by allowing the user to perform the action. Then the tool once the user prompts the finishing of the update/change version process will evaluate all of the files which have been modified or added and dump them into the Generated-GOG-Patch folder of your supplied Cold Steel directory. This is a safe measure against delayed GOG patches in the future, a friend is all you need (it took me 6 hours to find one :/).

Links
[Unofficial Patch Download] : mega.nz/#!q9JUlCjC!XFioQ5VToP4-PcFhIyrZ_mpTuXZyRa70P7j1LinndCk
[Binary] Cold Steel Delta Generator: cdn.discordapp.com/attachments/228687317026603009/345320899924459520/Release.7z
[Source Code] Cold Steel Delta Generator: cdn.discordapp.com/attachments/228687317026603009/345321003326636033/Cold-Steel-GOG-Delta-Update-Generator.7z
[Screenshot] Launcher: i.imgur.com/jILg15w.png
[Screenshot] Ingame: i.imgur.com/LUecIjh.png
[Screenshot] Options: i.imgur.com/GfBt4GT.png

So correct me if I'm wrong, but it's the Steam version also DRM free in this case then?

It is. http://www.neogaf.com/forum/showthread.php?p=245208897#post245208897

Yes, that's correct, this is the only reason why making this unofficial patch has been possible. The Steam and GOG versions of the game share one unified DRM-free executable, the same case has been with the Sky trilogy as of recent thanks to Sara's efforts (although not yet on GOG - only the Steam version has the GOG-Steam unified executable as of right now).

If the game had DRM, I would not be posting this. I could technically crack the executable myself if it did have but then when it would come to posting, that's I'm afraid would be outside of the line I have drawn for myself thus if the game had DRM it would not be something that I would have done.