I managed to fix the issue.
I was looking at the "Distant Guns RJW Enhanced" and "Jutland" folders in the "Storm Eagle Studios" folder and noticed that they have most of the same stuff in them. However most of the the sub-folders in "Jutland" have a 2 after them while the ones in "Distant Guns" do not. So I ran en experiment and copped those folders and the DG specific files over to the "Jutland" folder and then ran the DG_RJWp.exe in the "Jutland" folder and it ran just as it should, just with the Jutland splash screen but with the DG version number displayed in stead to the DG splash screen.
After that worked I created a new folder in the Storm Eagle Studios directory. I then moved the copies of the Battle Records, data, Installation Support, models, Music, Screenshots, Sound, and Textures folders to the new folder. Then copied everything not in a sub-folder from the Jutland folder to the new one as well. Removed the Jutland specific items and replaced them with their Distant Guns counterparts. Then I cut and pasted the official "Distant Guns RJWEnhanced" folder to another directory and renamed the new folder "Distant Guns RJWEnhanced". Result Distant Guns now works.
I did have an issue after I had done all of the above with StormPowered not recognizing Distant Guns and Jutland under the My Games tab however after uninstalling and reinstalling StormPowered it identified both of them perfectly and both of them now play.