Your priorities need to be:
Fit (getting you into fastest possible position)
Aerodynamics (kind of the point of the bike)
Weight (as you've asked)
I'd add durability as a honourable mention.
Fortunately it's possible to balance all those factors pretty well. I'd suggest not trying to save weight on shift components as you spend a lot for very little gain.
Cranks, wheels, bars are the components that can get really chunky. For a tri bike you'll need to pay attention to everything
Bars are tricky - usually lower weight means less adjustability - which can be fine if you know your position precisely, not so good if you need tilt or a specific setup - so you may have to make concessions there (because bars are about priority 1 and 2)
I built a 56 P3 and weighed as I went recently. I've added the changes I'd look at making if trying to get it lighter
I prefer not to save weight on consumables as it just means it costs more to keep running, but a 9000 cassette is a good weight saving for race wheels
I'd need to check on true weights before purchasing if I was doing it. And add pedals, cages etc
More could be saved on wheels but don't compromise aero or braking.
I'd expect the paint on a P3 to be closer to 400g than 300g, so stripping then clearcoating would save a lot and give you something unique (with no warranty)
Possible to save quite a bit on the bars - Tririg alpha X supposed to be ~650g (stem incl) but the fit range is quite specific so that may not be an option (an easy 200g loss if it is)
have a look at the project liberty write up on tririg for ideas.
You not going to get a really light beam bike. I'd start with Cervelo, QR or Orbea for this kind of project. That way you can build up something that doesn't have compromises (bad brakes, painful bars, hard to travel with etc).
