Hi Dmitry, thanks for looking!
Looking at the file properties via the bin folder the product version is 5.2.7-61128 for the System.Web.Http.dll.
Yes I manually deleted all items in the bin folder and obj folder and rebuilt several times now. However I didn't manually clean the build folder before first run, although I did use the 'rebuild' command after upgrading and before first run which cleans the bin prior to build.
From visual studio's point of view..
CMS project solution explorer reference properties: Version = 5.2.7.0, Path = C:\Files\Working Copies\LocalGitRepo\nas-websites\Nas.KenticoSites\packages\Microsoft.AspNet.WebApi.Core.5.2.7\lib\net45\System.Web.Http.dll
CMS project csproj file:
<Reference Include="System.Web.Http, Version=5.2.7.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35, processorArchitecture=MSIL">
CMS Web.Config binding redirect:
<assemblyIdentity name="System.Web.Http" publicKeyToken="31bf3856ad364e35" culture="neutral" />
<bindingRedirect oldVersion="0.0.0.0-5.2.7.0" newVersion="5.2.7.0" />
So that looks fine, and the CMS site runs ok. So the issue seems to be specifically the continuousintegration.exe that is created on build. I looked for any binding redirects in the ContinuousIntegration.exe.config file but there are no instances of any redirects for System.Web.Http