Ok, finalmente descobri por mim mesmo. O protocolo AJP funciona de maneira diferente das regras de tipo HTTP e, portanto, elas não se misturam. Para resolvê-lo, eu tive que parar de redirecionar tudo para o AJP e apenas redirecionar o aplicativo usando apenas o AJP. Aqui estava a resposta:
# don't ProxyPass through the "/" dir location,
# since it breaks the mod_rewrite rules
<Location /myapp>
ProxyPass ajp://localhost:8009/myapp
ProxyPassReverse ajp://localhost:8009/myapp
</Location>
RewriteEngine On
# rule to redirect from http to https
RewriteCond %{HTTPS} off
RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI}
# rule to redirect / to the app context since nothing is served at /
Redirect / /myapp?name=
# supplemental rules to handle URI shortcuts
RedirectMatch ^/(?i)name1 /myapp?name=NameOne
RedirectMatch ^/(?i)name2 "/myapp?name=Name%20Two"