This fixed it for me:
In .htaccess, I replaced…
# BEGIN W3TC Page Cache core
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^(.*\/)?w3tc_rewrite_test$ $1?w3tc_rewrite_test=1 [L]
RewriteCond %{HTTP:Accept-Encoding} gzip
RewriteRule .* - [E=W3TC_ENC:_gzip]
RewriteCond %{REQUEST_METHOD} !=POST
RewriteCond %{QUERY_STRING} =""
RewriteCond %{REQUEST_URI} \/$ [OR]
RewriteCond %{REQUEST_URI} (sitemap(_index)?\.xml(\.gz)?|[a-z0-9_\-]+-sitemap([0-9]+)?\.xml(\.gz)?) [NC]
RewriteCond %{REQUEST_URI} !(\/wp-admin\/|\/xmlrpc.php|\/wp-(app|cron|login|register|mail)\.php|\/feed\/|wp-.*\.php|index\.php) [NC,OR]
RewriteCond %{REQUEST_URI} (wp\-comments\-popup\.php|wp\-links\-opml\.php|wp\-locations\.php) [NC]
RewriteCond %{HTTP_COOKIE} !(comment_author|wp\-postpass|wordpress_\[a\-f0\-9\]\+|wordpress_logged_in) [NC]
RewriteCond %{HTTP_USER_AGENT} !(W3\ Total\ Cache/0\.9\.2\.4) [NC]
RewriteCond "%{DOCUMENT_ROOT}/wordpress/wp-content/w3tc/pgcache/%{REQUEST_URI}/_index%{ENV:W3TC_UA}%{ENV:W3TC_REF}%{ENV:W3TC_SSL}.html%{ENV:W3TC_ENC}" -f
RewriteRule .* "/wordpress/wp-content/w3tc/pgcache/%{REQUEST_URI}/_index%{ENV:W3TC_UA}%{ENV:W3TC_REF}%{ENV:W3TC_SSL}.html%{ENV:W3TC_ENC}" [L]
</IfModule>
# END W3TC Page Cache core
with…
# BEGIN W3TC Page Cache core
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^(.*\/)?w3tc_rewrite_test$ $1?w3tc_rewrite_test=1 [L]
#RewriteCond %{HTTP:Accept-Encoding} gzip
#RewriteRule .* - [E=W3TC_ENC:_gzip]
RewriteCond %{REQUEST_METHOD} !=POST
RewriteCond %{QUERY_STRING} =""
RewriteCond %{REQUEST_URI} \/$ [OR]
RewriteCond %{REQUEST_URI} (sitemap(_index)?\.xml(\.gz)?|[a-z0-9_\-]+-sitemap([0-9]+)?\.xml(\.gz)?) [NC]
RewriteCond %{REQUEST_URI} !(\/wp-admin\/|\/xmlrpc.php|\/wp-(app|cron|login|register|mail)\.php|\/feed\/|wp-.*\.php|index\.php) [NC,OR]
RewriteCond %{REQUEST_URI} (wp\-comments\-popup\.php|wp\-links\-opml\.php|wp\-locations\.php) [NC]
RewriteCond %{HTTP_COOKIE} !(comment_author|wp\-postpass|wordpress_\[a\-f0\-9\]\+|wordpress_logged_in) [NC]
RewriteCond %{HTTP_USER_AGENT} !(W3\ Total\ Cache/0\.9\.2\.4) [NC]
RewriteCond "%{DOCUMENT_ROOT}/wordpress/wp-content/w3tc/pgcache/%{REQUEST_URI}/_index%{ENV:W3TC_UA}%{ENV:W3TC_REF}%{ENV:W3TC_SSL}.html%{ENV:W3TC_ENC}" -f
RewriteRule .* "/wordpress/wp-content/w3tc/pgcache/%{REQUEST_URI}/_index%{ENV:W3TC_UA}%{ENV:W3TC_REF}%{ENV:W3TC_SSL}.html%{ENV:W3TC_ENC}" [L]
</IfModule>
# END W3TC Page Cache core
I think this means that my cached pages aren’t being gzipped, but at least now they are actually being cached and not regenerated each time.
Uncommenting these two lines, I get the “status: not cached” problem again:
#RewriteCond %{HTTP:Accept-Encoding} gzip
#RewriteRule .* - [E=W3TC_ENC:_gzip]