Here ya go mate, caching, fallback, all in a 15 lines of javascript. If you want to extract jquery out of there that should be easy enough.
No need for extra servers, the OPs guys don't even need to know it's there. Take an extra performance hit that is equal to loading another image per page (yeah image requests, while probably served from CDN, also include an accurate Date response header as I checked), cached for 7 days (remove the cookie during periods of daylight saving times etc). Just have to make sure the server time is reasonably accurate. I'm sure a few seconds inaccuracy wouldn't matter.
window.getLocalUnixTime = ->
(new Date()).getTime()
window.loadTime = (callback) ->
if $.cookie("time-drift-delta")
callback(getLocalUnixTime() + parseInt($.cookie("time-drift-delta"), 10))
else
$.ajax window.location,
type: "HEAD"
success: (data, status, jqXHR) ->
datetime = new Date(jqXHR.getResponseHeader("Date"))
$.cookie("time-drift-delta", datetime.getTime() - getLocalUnixTime(), {expires: 7})
callback datetime
fail: ->
callback getLocalUnixTime()