So...it took me a lot of playtesting to replicate your error:-

I got this error due to removing the Faction ShipStyle and ShipDefs xmls from the directory, so basicly they were not presant when I booted the game. I would check the location of your files. And or the name of your Ship Style.

Please start a support ticket so we can assist further.

https://esupport.stardock.com/index.php?/Tickets/Submit

Are you running 3.0 or 4.0 of gaintlets race mod. Are you using 1.6 or 1.7 of the game.

Dropbox or Onedrive?

Did you rename the files outside of the designer by anychance? There seems to be something badly wrong with the designs:-

 

Debug Message:  IShipDesignGfxUpdater::SendEvent_UpdateGfxData: Failed to find object config with name: Leviathan Dreadnought_668584E70FDA43C8BB69B241FBC5662F.objgfxcfg
Debug Message:  CShipDesignGfxListenerBase: Failed because root component was NULL.  Did an objgfxcfg '(null)' fail to load?

Is the error I get for all the designs you posted the link too. They do not even marry up with the names of the files:-

UnsomnonDreadnought_668584E70FDA43C8BB69B241FBC5662F

When in the designer the designs just show up as blank, and cause a CTD if selected. This is the issue you are having??

There is also a 4th file, file name GC3WSDATA for each design which is baffling to me as I only ever get 3 files after saving a template in the designer, if I leave the files with GCWSDATA in the design folder then none of your designs show up and when i then check the folder for the designs they are gone, I'm guessing this file is linked to steam workshop and since I am not subscribed to said designs they get removed?

After downloading designs off the workshop, boot up the game, goto options make sure "Show all Designs" is checked, start a game with say the Yor, navigate to the designs you downloaded(under the downloaded tab), save each design as a template, with your new file name. You then use the Yor as your base, if you do not do this you have no idea what base the author used when he created his designs, and that in its self causes issues:-

    <InternalName>UnsomnonShipStyleSet</InternalName>
    <DisplayName>Unsomnon Style</DisplayName>
    <Icon>GC3_S_Basic_Ship_Icon.png</Icon>
    <DisplaySampleObjGfxConfig>UnsomnonCorvette_EFB00F8F995E42D1AE584CE6841ACEC7.objgfxcfg</DisplaySampleObjGfxConfig>
    <ShipStyle>Yor</ShipStyle>
    <PartsStyle>Yor</PartsStyle>
    <StartingShipyard>BasicShipyard</StartingShipyard>

Thanks guys, I will give your suggestions a look. 

admiralWillyWilber: can you tell where are the shipclassdef files and shipstyle files are in Gauntlet 4.0? Can't seem to get my hands on them