Advanced Search dialog is slow to load on an instance with a large number of custom fields

On our JIRA 4.0 instance, starting a new Simple search requires only a 1.5 second page load time whereas switching to Advanced mode takes 8 seconds. This 8 second tax is also present when viewing any search results in the Issue Navigator while in Advanced Search mode. Looking at the HTML for the Advanced Search page, I see a large div called "jqlFieldz", and I assume it is the generation of this div that is causing the performance slowdown.

For the record I see that j.a.c.'s jqlFieldz div is 18499 bytes long while ours is 122267 bytes long. Our JIRA instance has 518 custom fields.