Kirk,
In regards to the IRL engagement/use of the ATS, I've never heard of any technique or SOP whereupon TOGA is selected on the runway as the throttles are manually advanced through 25%. Would need more context to better understand.
Typical SOP dictates we wait until taking the runway to select TOGA / N1 TO to avoid an unintended engagement of the ATS during taxi/ (although TOGA / N1 TO is often selected during taxi to the runway despite SOP) We can save that 'normalization of deviation' discussion for another day.
2 methods to engage ATS for TO that are commonly known or used IRL: (prerequisite = the ATS MSD indicates N1 TO)
Slowly advance the power levels manually until ATS engagement (75% N1) - and thence let the ATS set TO thrust - with the PM checking that TO thrust has indeed been achieved by 80 knots. (most common).
Press the ATS engagement button when on the runway and cleared for takeoff - and let the ATS take them all the way from idle up to TO thrust. (rare)
My observation from your video is that you are advancing the thrust levers manually and quite aggressively compared to IRL. We do not advance the thrust levers that quickly. We also do not 'firewall' the throttles and rely on the ATS to trim or set power - that technique would probably trigger exceedances similar to your video.
Reference this video from the 2 minute mark. I'd say this is very representative of a typical CL60 ATS takeoff IRL:
From initial advancement of thrust levers to ATS engagement is about 7 seconds. (green lights illuminate either side ATS engagement button) Total time from initial advance of thrust levers to takeoff thrust is about 11 seconds. (vs about 4 seconds in your video) Time to 80 knots is about 14 seconds give or take.
The point I'm moving towards is that ATS on this airframe was an afterthought/option that is not fully integrated. I think of the ATS as a 'helper' that has to be managed. The ATS IRL does some odd stuff - and we have to keep an eye on it. It often will overshoot the thrust targets, it won't keep up during approaches on gusty days, it won't keep up with speed changes, especially on the mach to IAS transition during descent. Then there's the airframe specific 'oddities' - such as ours where the throttles will split at low power settings triggering an occasional ATS disconnect. We have to help it / manage it quite a bit. The ATS limitations on the CL60 illustrate it's helper status. We can't use them for GA, CAT II, APR, steep approaches, or touch and goes. (to name a few, the list has 16 or so bullets)
As such - relying on the ATS to trim thrust or prevent an exceedance on takeoff by firewalling the throttles - you're seeing what would probably happen IRL.
I see you've troubleshot the ATS disengagement down to a saved state root cause - but if your goal is to emulate IRL technique - I hope this information will be helpful.