Update:

I now have all three original Cossacks games and both American Conquest games working almost perfectly both on GOG and Steam. For all of these games except the Steam version of Cossacks: Back to War, the trick that seems to work best for me is to replace mdraw.dll with the ddraw.dll file from dgVoodoo 2 inside the game directories, and configuring dgVoodoo to run with scaling set to "Stretched, keep Aspect Ratio".

With Cossacks: Back to War for Steam, there is no mdraw.dll file to replace, and putting ddraw.dll from dgVoodoo 2 in the game directory is not having any effect. I did however find that it works if I used the dgVoodoo 2 driver to replace ddraw.dll in the Windows\SysWOW64 directory. I attempted to use Narzoul's suggested trick of including a manifest file to force the usage of ddraw.dll from the local directory but it didn't work, however I have yet to try his suggested registry trick which I will be testing shortly.

Assuming I can get the Steam version of Cossacks: Back to War to use the local ddraw.dll file from dgVoodoo 2, the only remaining issue would be getting proper intro video playback for American Conquest and American Conquest: Fight Back. Right now when I run them with the dgVoodoo 2 ddraw drivers, the videos are blacked out with only sound being provided. I'm able to watch these videos using Media Player Classic running with older Cinepak codecs, but dgVoodoo 2 apparently still has issues with certain video formats. I attempted to re-encode the videos but this only caused them to instantly crash on playback in-game, however there are still some more tricks for me to try.

Once I've finished with my dgVoodoo testing and tweaking, I will try out the latest patch suggestion from the GOG staff and run Narzoul's DDraw Compat with full debugging as promised.

Update:

I've completed generating output for Narzoul's DDraw Compat drivers in debug mode for Cossacks: Art of War and will hopefully be sending it to him soon. I also tested the following community-made patch for Cossacks: Back to War as recommended by Falran from the GOG staff:

https://github.com/ereb-thanatos/cossacks-revamp-2017

This community patch works well on my system although it's missing the intro videos, game music and also includes many alterations to the gameplay. It appears to be a standalone DRM-free patch, meaning you don't require an existing Cossacks: Back to War installation in order to run and play it.

I believe at this time the most authentic recreation of the original game experience on my system is achieved by using the dgVoodoo 2 driver set, taking the ddraw.dll file and using it to replace mdraw.dll, combined with using the driver customization features to set their scaling mode as "Stretched, keep Aspect Ratio".

The dgVoodoo 2 fix gets all three Cossacks 1 titles and both American Conquest titles working seemingly perfectly for me with the GOG versions, and all of these titles except Cossacks: Back to War working with the Steam versions. For this last title on Steam, one working fix is to use the dgVoodoo 2 ddraw.dll drivers as a direct replacement for ddraw.dll in the Windows\SysWOW64 directory, combined with the same custom settings as before.

Ideally for this last case, a shim file such as dciman32.dll would be created to redirect file usage to ddraw.dll in the local directory, or the shim could itself include the necessary substitute DirectDraw instructions, but I'm not knowledgeable enough as of yet to do this myself in Windows 10. For earlier versions of Windows there was a Microsoft tool called the Application Compatibility Toolkit which could be used to create compatibility shims with file redirections as needed, but it doesn't appear to be available for recent builds of Windows 10. For Windows 10 it appears that a shim creation capability may be provided by the Windows Assessment and Deployment Kit, but I haven't yet had a chance to familiarize myself with this tool. In any case this issue is of minimal concern to GOG users as it only applies to the Steam version, and I prefer the GOG version myself.

Lastly there's the issue of getting the intro videos working with both American Conquest titles. I found that I wasn't able to get these videos working neither with dgVoodoo 2 nor with DxWnd, although the games themselves seem to work fine. Instead of my computer playing the videos correctly, I simply get a black screen with the movie soundtrack playing, although the video files themselves work fine when I play them in Media Player Classic. Re-encoding the videos didn't seem to help, it just made them crash and the game would load right away instead, but I won't pretend that I tried every possible scenario with this and if anyone knows what to do, advice would be much appreciated.

I believe the intro video issues with the American Conquest games is related to video playback issues with dgVoodoo 2 and DxWnd, but I will need to inquire with their respective developers to check. One existing recommended workaround for similar video issues with other games is to run the games in windowed mode rather than fullscreen, however for whatever reason I haven't been successful in doing this with either dgVoodoo 2 nor DxWnd for any of these GSC titles, they seem to always load into fullscreen no matter what options I select. Again, any advice to put me on the right track would be greatly appreciated.

Thankfully I found a decent workaround for the American Conquest video issues, and it turns out to be the same thing that the Cossacks 1 games for GOG do by default. It appears that when you launch the Cossacks 1 games via the default shortcuts provided by GOG, rather than launching dmcr.exe they launch cossacks.exe with appropriate command line arguments instead. cossacks.exe itself appears to be some sort of combined video player and launcher whose job is to play the intro videos and then launch the main game. When I took the cossacks.exe file from the Cossacks 1 games and transferred it to the American Conquest directories, and modified the launch shortcuts accordingly, I was able to get the American Conquest intro videos playing successfully followed by having the games launch normally, although they do still attempt to play the intro videos through the games themselves, leading to the aforementioned black screen issues (it's easy enough to just skip them and go straight to the menu, of course).

At this point I'm not sure what else I can do to help get these games running as good as new on the latest modern systems, but I'm pretty happy with the working state on my own system for now. If I have any major updates to add it will probably be related to whatever feedback I can obtain from the developers of dgVoodoo 2 and DxWnd. As always, all help and suggestions are still very much welcome and appreciated.

Critical Update

I had a brief chat with Narzoul and it turns out at least in my case there is actually a very simple solution, I've been using a jackhammer when only a screwdriver is required. In Windows 10 there's no option provided by the OS for setting custom resolutions, nor are such settings available for my NVIDIA card as has been the case in past versions. However it turns out that custom resolutions for my system can be implemented via the Intel Graphics settings panel.

Upon making the 1024x768 resolution available in the Intel Graphics panel, it becomes available as an option for my Windows 10 standard resolution and I'm now able to launch and play all of the Cossacks and American Conquest games without any file modifications whatsoever. The only game alteration needed to make the games run optimally is to set dmcr.exe to run in Windows 8 compatibility mode, although curiously this change isn't needed with the GOG version of Cossacks: Art of War.

Hopefully my investigations into using DirectDraw substitutes will prove useful if any further problems arise running these games on newer systems, but for the time being I believe my issues can be marked as resolved and I credit Narzoul with finding the solution.

Thanks everyone for all your help and please feel free to send me any questions or suggestions if there's more you'd like to discuss.

Thank you all for your hard work on this!