Running Ableton with Ardour and Jack OS?

I apologize if this has been covered in past forums. I looked but did not find, so here I am hoping you all can help.
I have had no problem syncing up Ardour, Jack, and Hydrogen, but have had no such luck with Ableton Live. I am finding no option in Ableton’s audio preferences to choose Jack, only the generic “aggregate device.” I’m pretty sure that all my other preferences are set correctly because, as I said, everything else is syncing just fine.
My setup:
MacOS 10.4.11, intel duo
Ardour 2.4.1
Latest JackOS
Ableton 4 (I know, I know, it’s really old, but still works okay!)

I love recording in Ardour and was getting excited to start taking advantage of Jack’s full capapbilities, so please, please, any thoughts are greatly appreciated. Anything?
Thanks in advance.

You must have JACK already running for CoreAudio-based applications to be able to see it and choose it as an input/output device. I am aware of only such application that cannot use JACK in this way, and it is not Live.

Regarding “sync” in the sense of the shared transport control that JACK offers, please read my response to this forum post.

Hi Paul,
Thanks for your response and thanks even more for your great work on Ardour and JACK. I was using the term “sync” improperly in my first post, though your link to syncing transports will be extremely helpful as I play with Hydrogen further. Thanks for that.
As for Live, like you suggested, I have been starting JACK prior to opening Live, but with no luck. I’m not really sure where else I might look for my error. But here are some things I’ve tried…
I thought, ‘Could it be something in my Audio MIDI Setup?’ so in the Audio MIDI Setup window I have tried two different things with the system settings: having the default input and default output both set to “aggregate device” and then both set to “jack router.” Neither setting makes a difference to Live, and I can’t think of anything else to try here.
As for my Live preferences, CoreAudio is set as the driver type by default, but I am getting no option for JACK as either the input or output audio device. I haven’t played with the “Settings” section where there are options for Input and Output Configurations, but again, there is no option for JACK here. Is it possible that my ancient version of Live (version 4) does not recognize JACK even with my Audio MIDI device setup as described above?
And still nothing showing up in JackPilot’s Routing lists or Ardour’s input options. Could there be something else I’m overlooking? Thanks again for any help.