This is the Omega FPB lifter and sear configuration at rest, with the trigger bar engagement surface in green and the lifter/sear engagement surface in red.

Now, as you can see, the lifter must be moved to begin engaging the sear at all. Here is the point at which the lifter actually begins engaging the sear.

So, one solution for removing some of the take-up is to lock the lifter in this position (such as pinning it in place against the sear). However, this cannot be safely done without further modification because having the lifter in its fully engaged position will prevent proper slide function. Thus we have this possible solution, which has previously been suggested:

Here, the lifter would be pinned to the sear (or otherwise kept in this position at rest), the actual lifter portion removed, and the FPB itself removed from the slide. The downsides to this modification are 1) that you must permanently modify the lifter (and sear, if the lifter is pinned to it) in a fairly radical way and 2) you must remove the FPB altogether. The first part is even more of an issue when you take into account the fact that we do not yet have readily available factory replacement parts for the Omega mechanism. So if you screw anything up, you are absolutely and completely SOL until spare lifters and/or sears are available.
Since the lifter movement that occurs before sear engagement accounts for roughly 40% of the total take-up in SA, it would be impossible to remove 90% of the take-up without pinning or otherwise locking the lifter in a pre-engaged state while at rest, which I had already mentioned in my original post.
Removing the true take-up (the travel before engaging the lifter) could be accomplished in three ways (or a combination thereof) - adding material to the end of the trigger bar, adding material to the trigger bar engagement surface of the lifter, or modifying the connector to position the trigger bar further back upon reset in SA.