Creating a second admin domain for CMS access

I’m running a multisite WordPress installation hosting about 100 sites. Here is my intended setup for production: one server running ARR on IIS sitting in front of servers that only respond to HTTPS requests for the CMS.

The CMS server in my lab is running https://www.wordpress.dev. The ARR server receives requests for https://www.wordpress.cms.dev and forwards the request with the host header https://www.wordpress.dev and rewrites the outbound content replacing https://www.wordpress.dev with https://www.wordpress.cms.dev. So far, so good. The problem comes when I try to hit https://www.wordpress.cms.dev/wp-admin/. This issues a 302 redirect to https://www.wordpress.dev/wp-login.php?redirect_to=https%3A%2F%2Fwww.wordpress.dev%2Fwp-admin%2F&reauth=1.

Here are my current rewrite rules on the ARR server:

<rewrite>
            <globalRules>
                <clear />
                <rule name="ARR_wordpress_loadbalance" patternSyntax="Wildcard" stopProcessing="true">
                    <match url="*" />
                    <conditions logicalGrouping="MatchAll" trackAllCaptures="false">
                        <add input="{HTTP_HOST}" pattern="*.wordpress.dev" />
                        <add input="{SERVER_PORT}" pattern="80" />
                    </conditions>
                    <action type="Rewrite" url="http://wordpress/{R:0}" />
                </rule>
                <rule name="ARR_wordpress-ssl_loadbalance" enabled="true" patternSyntax="Wildcard" stopProcessing="true">
                    <match url="*" />
                    <conditions logicalGrouping="MatchAll" trackAllCaptures="true">
                        <add input="{OriginServers:{HTTP_HOST}}" pattern="*" />
                        <add input="{HTTPS}" pattern="on" />
                    </conditions>
                    <action type="Rewrite" url="https://wordpress-ssl/{R:0}" />
                    <serverVariables>
                        <set name="HTTP_X_FORWARDED_HOST" value="{HTTP_HOST}" />
                        <set name="HTTP_HOST" value="{C:1}" />
                    </serverVariables>
                </rule>
            </globalRules>
            <rewriteMaps>
                <rewriteMap name="OriginServers">
                    <add key="www.wordpress.cms.dev" value="www.wordpress.dev" />
                </rewriteMap>
                <rewriteMap name="OutboundMap">
                    <add key="www.wordpress.dev" value="www.wordpress.cms.dev" />
                </rewriteMap>
            </rewriteMaps>
            <allowedServerVariables>
                <add name="HTTP_HOST" />
                <add name="HTTP_X_FORWARDED_HOST" />
            </allowedServerVariables>
            <outboundRules>
                <rule name="Outbound Rule" preCondition="IsHTTPS" enabled="true" patternSyntax="Wildcard">
                    <match filterByTags="A, Area, Base, Form, Frame, Head, IFrame, Img, Input, Link, Script" pattern="https://*/*" />
                    <conditions trackAllCaptures="false">
                        <add input="{OutboundMap:{R:1}}" pattern="*" />
                    </conditions>
                    <action type="Rewrite" value="https://{C:1}/{R:2}" />
                </rule>
            </outboundRules>
        </rewrite>
        <proxy enabled="false" preserveHostHeader="false">
            <cache enabled="false" />
        </proxy>

Any assistance would be greatly appreciated.