This whole timing issue is also a pita with regards to synced effects like stutter / mangling /repeat effects e.g Cableguys Volumeshaper. Volumeshaper behaves totally unpredictable as it simply does not get proper timing info from Live if the project is anything but a basic template. Doing hard cuts and precise side-chain mimicking is unreliable, as any changes to the effect path might move the timing around. This defeats the purpose of host-synced effects, as they are in many occasions simply NOT sync. In live performances tight cuts and on beat syncing / looping could be regarded as obligatory for such an application.
Please strongly consider putting some effort into adding to Live what is completely standard behavior in other hosts. since years.
Thanks!