A reply in the article Stephen Muecke commented with got me started in the right direction. The solution is a mix of probably my confusion of which config needs to be where, and what feels like a workaround to something...
Set the [Output Path] of your class library project to [bin/]. Mohammad Chehab mentions this in his (currently offline?) blog post which was referenced in this article: http://thetoeb.de/2014/01/05/enabling-mvc5-intellisense-in-a-classlibrary-project/
In your [ClassLibrary/Views] folder you should have a Web.config which includes the correct razor versions and namespaces. I just copied the contents of the Web.config from our working Web application project and added/changed some namespaces. Example below.
In your [ClassLibrary] root folder you should change the App.config so that it also contains the system.web section with the compilation setting. Example below.
After changing these to a clean, close the solution, delete the bin folders, open the solution and for me it finally all worked again.
I do have a sporadic issue with System.Web.Mvc.xml being locked, perhaps a side effect of the output path change that MS did not foresee or something... Perhaps nothing to worry about.
Hope this helps some poor googling soul some day.
Project/Views/Web.config
<?xml version="1.0"?>
<configuration>
<configSections>
<sectionGroup name="system.web.webPages.razor" type="System.Web.WebPages.Razor.Configuration.RazorWebSectionGroup, System.Web.WebPages.Razor, Version=3.0.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35">
<section name="host" type="System.Web.WebPages.Razor.Configuration.HostSection, System.Web.WebPages.Razor, Version=3.0.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35" requirePermission="false" />
<section name="pages" type="System.Web.WebPages.Razor.Configuration.RazorPagesSection, System.Web.WebPages.Razor, Version=3.0.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35" requirePermission="false" />
</sectionGroup>
</configSections>
<system.web.webPages.razor>
<host factoryType="System.Web.Mvc.MvcWebRazorHostFactory, System.Web.Mvc, Version=5.2.3.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35" />
<pages pageBaseType="System.Web.Mvc.WebViewPage">
<namespaces>
<add namespace="System.Web.Mvc" />
<add namespace="System.Web.Mvc.Ajax" />
<add namespace="System.Web.Mvc.Html" />
<add namespace="System.Web.Optimization"/>
<add namespace="System.Web.Routing" />
</namespaces>
</pages>
</system.web.webPages.razor>
<appSettings>
<add key="webpages:Enabled" value="false" />
</appSettings>
<system.webServer>
<handlers>
<remove name="BlockViewHandler"/>
<add name="BlockViewHandler" path="*" verb="*" preCondition="integratedMode" type="System.Web.HttpNotFoundHandler" />
</handlers>
</system.webServer>
<system.web>
<compilation>
<assemblies>
<add assembly="System.Web.Mvc, Version=5.2.3.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35" />
</assemblies>
</compilation>
</system.web>
</configuration>
Project/App.config
<?xml version="1.0" encoding="utf-8"?>
<!--
For more information on how to configure your ASP.NET application, please visit
http://go.microsoft.com/fwlink/?LinkId=301880
-->
<configuration>
<system.web>
<compilation debug="true" targetFramework="4.6" />
</system.web>
<runtime>
<assemblyBinding xmlns="urn:schemas-microsoft-com:asm.v1">
<dependentAssembly>
<assemblyIdentity name="Microsoft.Owin.Security" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="0.0.0.0-3.0.1.0" newVersion="3.0.1.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="Microsoft.Owin.Security.OAuth" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="0.0.0.0-3.0.1.0" newVersion="3.0.1.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="Microsoft.Owin.Security.Cookies" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="0.0.0.0-3.0.1.0" newVersion="3.0.1.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="Microsoft.Owin" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="0.0.0.0-3.0.1.0" newVersion="3.0.1.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="Newtonsoft.Json" culture="neutral" publicKeyToken="30ad4fe6b2a6aeed" />
<bindingRedirect oldVersion="0.0.0.0-7.0.0.0" newVersion="7.0.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="System.Web.Optimization" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-1.1.0.0" newVersion="1.1.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="WebGrease" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="0.0.0.0-1.5.2.14234" newVersion="1.5.2.14234" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="System.Web.Helpers" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-3.0.0.0" newVersion="3.0.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="System.Web.Mvc" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-5.2.3.0" newVersion="5.2.3.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="System.Web.WebPages" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-3.0.0.0" newVersion="3.0.0.0" />
</dependentAssembly>
</assemblyBinding>
</runtime>
</configuration>
