Object reference not set to an instance of an object.

[NullReferenceException: Object reference not set to an instance of an object.]   GleamTech.AspNet.UI.ComponentStateManager.SaveState(String stateId, ComponentState state) +66   GleamTech.AspNet.UI.ComponentRenderer.SaveState(StatefulComponent statefulComponent, String requestPath) +238   System.Web.UI.Control.PreRenderRecursiveInternal() +161   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint) +6874

Server Error in '/' Application.

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Object reference not set to an instance of an object.

[NullReferenceException: Object reference not set to an instance of an object.]   GleamTech.AspNet.UI.ComponentStateManager.SaveState(String stateId, ComponentState state) +66   GleamTech.AspNet.UI.ComponentRenderer.SaveState(StatefulComponent statefulComponent, String requestPath) +238   System.Web.UI.Control.PreRenderRecursiveInternal() +161   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Control.PreRenderRecursiveInternal() +255   System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint) +6874

GleamTech.DocumentUltimate.AspNet.NetFramework.WebActivation.PreApplicationStart();

Cannot register a module after the application has been initialized.

[InvalidOperationException: Cannot register a module after the application has been initialized.]   System.Web.DynamicModuleRegistry.Add(Type moduleType) +244   System.Web.HttpApplication.RegisterModule(Type moduleType) +75   GleamTech.AspNet.NetFramework.WebActivation.PreApplicationStart() +404   GleamTech.DocumentUltimate.AspNet.NetFramework.WebActivation.PreApplicationStart() +52   GleanTechModule.Application_BeginRequest(Object source, EventArgs e) +42   System.Web.SyncEventExecutionStep.System.Web.HttpApplication.IExecutionStep.Execute() +139   System.Web.HttpApplication.ExecuteStepImpl(IExecutionStep step) +195   System.Web.HttpApplication.ExecuteStep(IExecutionStep step, Boolean& completedSynchronously) +88

The global.asax doesn't seem to be the best solution to do this because of the deployment issues described in the question.

A viable solution is implementing this in a httpmodule

The init method can be used to wire everything up since this is called when the sharepoint application starts.

the httpmodule can be added in the web.config by a feature receiver

This way there is no need to do tricks with the global.asax that is located in a directory you can't deploy to with a feature and you have all the functionality and correct time to instantiate the DI container.

using System.Web;

public class GlobalHttpModule : IHttpModule
{
    public void Init(HttpApplication app)
    {
        //The init method can be used to wire everything up since this is called when the Sharepoint application starts.

        GleamTech.DocumentUltimate.AspNet.NetFramework.WebActivation.PreApplicationStart();
    }

    public void Dispose()
    {
    }
}

public class GlobalHttpModuleFeature : SPFeatureReceiver
{
    private readonly Type targetHttpModuleType = typeof(GlobalHttpModule);

    public override void FeatureActivated(SPFeatureReceiverProperties properties)
    {
        var webApp = properties.Feature.Parent as SPWebApplication;

        var modification = GetModification();

        webApp.WebConfigModifications.Add(modification);
        webApp.Update();

        webApp.WebService.ApplyWebConfigModifications();
    }

    public override void FeatureDeactivating(SPFeatureReceiverProperties properties)
    {
        var webApp = properties.Feature.Parent as SPWebApplication;

        var modification = GetModification();

        webApp.WebConfigModifications.Remove(modification);
        webApp.Update();

        webApp.WebService.ApplyWebConfigModifications();
    }

    private SPWebConfigModification GetModification()
    {
        var modification = new SPWebConfigModification(
            string.Format("add[@name='{0}']", targetHttpModuleType.Name), 
            "configuration/system.webServer/modules"
        );
        modification.Sequence = 0;
        modification.Type = SPWebConfigModification.SPWebConfigModificationType.EnsureChildNode;
        modification.Value = string.Format(
            @"<add name=""{0}"" type=""{1}"" />",
            targetHttpModuleType.Name,
            targetHttpModuleType.AssemblyQualifiedName);
    }
}

GleamTech.DocumentUltimate.AspNet.NetFramework.WebActivation.PreApplicationStart() +52   GleanTechModule.Application_BeginRequest(Object source, EventArgs e) +42