Refactoring duplicate custom service configuration in .NET core

In my current .NET Core project, I want to inject two services into my controllers for dependency injection.

I wrote the following extension methods that each takes a IConfigurationSection, sets up the corresponding ldapContext and adds it to the services collection:

public class Startup
{
    public void ConfigureServices(IServiceCollection services)
    {
        var authenticationLdapConfiguration = Configuration.GetSection("AuthenticationLdap");
        services.ConfigureAuthenticationLdapServer(authenticationLdapConfiguration);
        var shibAttribLdapConfiguration = Configuration.GetSection("ShibbolethAttributesLdap");
        services.ConfigureShibbolethAttributeLdapServer(shibAttribLdapConfiguration);
    }
}

public static class ServiceCollectionExtensions
{
    public static void ConfigureAuthenticationLdapServer(this IServiceCollection services, IConfigurationSection authLdapConfiguration)
    {
        var ldapConnectionInfo = createLdapConnectionInfo(authLdapConfiguration);
        IAuthenticationLdapContext ldapContext = new AuthenticationLdapContext(ldapConnectionInfo);

        ldapContext.Bind();

        services.AddSingleton<IAuthenticationLdapContext>(ldapContext);
    }


    public static void ConfigureShibbolethAttributeLdapServer(this IServiceCollection services, IConfigurationSection shibAttribsLdapConfiguration)
    {
        var ldapConnectionInfo = createLdapConnectionInfo(shibAttribsLdapConfiguration);
        IShibbolethAttributeLdapContext ldapContext = new ShibbolethAttributeLdapContext(ldapConnectionInfo);

        ldapContext.Bind();

        services.AddSingleton<IShibbolethAttributeLdapContext>(ldapContext);
    }

    private static LdapConnectionInfo createLdapConnectionInfo(IConfigurationSection ldapServerConfiguration)
    {
        //set up connection info
    }
}

public interface IShibbolethAttributeLdapContext : ILdapContext {}

public interface IAuthenticationLdapContext : ILdapContext {}

public interface ILdapContext 
{
    //signatures of the functionality implemented below
    void Bind();
}

public class LdapContext : ILdapContext 
{
    public LdapContext(LdapConnectionInfo ldapConnectionInfo) { }
    //lots of functionality that I ultimately need
    public void Bind(){}
}

public class ShibbolethAttributeLdapContext : LdapContext, IShibbolethAttributeLdapContext
{
    public ShibbolethAttributeLdapContext(LdapConnectionInfo ldapConnectionInfo) : base(ldapConnectionInfo) {}
}

public class AuthenticationLdapContext : LdapContext, IAuthenticationLdapContext
{
    public AuthenticationLdapContext(LdapConnectionInfo ldapConnectionInfo) : base(ldapConnectionInfo) {}
}

I cannot change ILdapContext nor LdapContext as they are from an assembly that I don't manage.

Obviously, these methods only differ in the types that they wire up. Is there an elegant way to remove this duplication? My guess was to use generics or maybe a func, but I didn't come up with a solution.

UPDATE:
So I came up with this solution over the weekend that gets rid of the static extension methods as suggested by kayess:

public class Startup
{
    public IConfigurationRoot Configuration { get; }

    // This method gets called by the runtime. Use this method to add services to the container.
    public void ConfigureServices(IServiceCollection services)
    {
        //set up services

        var authLdapContext = createBoundLdapContext<AuthenticationLdapContext>(Configuration.GetSection("AuthServer"));
        services.AddSingleton<IAuthenticationLdapContext>(authLdapContext);
        var shibbAttribLdapContext = createBoundLdapContext<ShibbolethAttributeLdapContext>(Configuration.GetSection("ShibAttribServer"));
        services.AddSingleton<IShibbolethAttributeLdapContext>(shibbAttribLdapContext);

    }

    private TContextInstance createBoundLdapContext<TContextInstance>(IConfigurationSection ldapServerConfiguration)
    where TContextInstance : LdapContext
    {
        TContextInstance ldapContext = createLdapContext<TContextInstance>(ldapServerConfiguration);

        ldapContext.Bind();

        return ldapContext;
    }

    private TContextInstance createLdapContext<TContextInstance>(IConfigurationSection ldapServerConfiguration) 
    where TContextInstance : LdapContext
    {
        var ldapConnectioninfo = createLdapConnectionInfo(ldapServerConfiguration);
        TContextInstance ldapContext = (TContextInstance)Activator.CreateInstance(typeof(TContextInstance), ldapConnectioninfo);

        return ldapContext;
    }

    private LdapConnectionInfo createLdapConnectionInfo(IConfigurationSection ldapServerConfiguration)
    {
        var ldapConnectionInfo = new LdapConnectionInfo();
        //set up ldapConnectionInfo
        return ldapConnectionInfo;
    }
}

Can I make it better?