I'm trying to force caching of a very obnoxious piece of PHP script which actively tries to resist caching for no good reason by actively setting all the anti-cache headers:

Cache-Control: no-store, no-cache, must-revalidate, post-check=0, pre-check=0
Content-Type:  text/html; charset=UTF-8
Date:          Thu, 22 May 2014 08:43:53 GMT
Expires:       Thu, 19 Nov 1981 08:52:00 GMT
Last-Modified: 
Pragma:        no-cache
Set-Cookie:    ECSESSID=...; path=/
Vary:          User-Agent,Accept-Encoding
Server:        Apache/2.4.6 (Ubuntu)
X-Powered-By:  PHP/5.5.3-1ubuntu2.3

If at all avoidable I do not want to have to modify this 3rd party piece of code at all and instead just get Apache to cache the page for a while. I'm doing this very selectively to only very specific pages which have no real impact on session cookies or the like, i.e. which do not contain any personalised information.

CacheDefaultExpire      600
CacheMinExpire          600
CacheMaxExpire          1800
CacheHeader             On
CacheDetailHeader       On
CacheIgnoreHeaders      Set-Cookie
CacheIgnoreCacheControl On
CacheIgnoreNoLastMod    On
CacheStoreExpired       On
CacheStoreNoStore       On
CacheLock               On

CacheEnable disk /the/script.php

Apache is caching the page alright:

[cache:debug] AH00698: cache: Key for entity /the/script.php?(null) is http://example.com:80/the/script.php?
[cache_disk:debug] AH00709: Recalled cached URL info header http://example.com:80/the/script.php?
[cache_disk:debug] AH00720: Recalled headers for URL http://example.com:80/the/script.php?
[cache:debug] AH00695: Cached response for /the/script.php isn't fresh. Adding conditional request headers.
[cache:debug] AH00750: Adding CACHE_SAVE filter for /the/script.php
[cache:debug] AH00751: Adding CACHE_REMOVE_URL filter for /the/script.php
[cache:debug] AH00769: cache: Caching url: /the/script.php
[cache:debug] AH00770: cache: Removing CACHE_REMOVE_URL filter.
[cache_disk:debug] AH00737: commit_entity: Headers and body for URL http://example.com:80/the/script.php? cached.

However, it is always insisting that the "cached response isn't fresh" and is never serving the cached version. I guess this has to do with the Expires header, which marks the document as expired (but I don't know whether that's the correct assumption). I've tried to overwrite and unset headers using mod_headers, but this doesn't help; whatever combination I try the cache is not impressed at all. I'm guessing that the order of operation is wrong, and headers are being rewritten after the cache sees them. early header processing doesn't help either. I've experimented with CacheQuickHandler Off and trying to set explicit filter chains, but nothing is helping. But I'm really mostly poking in the dark, as I do not have a lot of experience with configuring Apache filter chains.

Is there a straight forward solution for how to cache this obnoxious piece of code?