...it may be moot now that you have done a fast run, but I thought I recalled that the primary triggers were killing the basic Collectors in each wave, with possibly a secondary time based trigger. The final trigger is of course killing all hostiles (to end the section). I would need to mess around with it to make sure the time trigger actually exists, it has been a while.
I think each wave is triggered when the number of enemies drops below a certain number (like the Object Rho scenario). For example, I noticed (during an engineer run) that the last platform does not appear if a scion and harbi (or two scions) are on the map at the same time (2 heavy enemies). So I'm guessing the threshold is 2. What I don't know is whether ordinary mooks and heavy units are weighted the same in this count. Also, I have not tested whether events are triggered when an enemy is "removed" by stasis (as is known to occur at the end of a scenario). If correct, then the key to speed is eliminating all but one enemy in each wave ASAP so as to trigger the next platform (hence the GPS + squad-based warp bomb). This means that other classes besides adept should be able to do this provided they take stasis as a bonus power.
The issue there would be finding a way (besides singularity) to pin the first harbi down without killing him so he does not show up on a subsequent platform to gum up the works. Engineer with combat drone perhaps? Or send in a squad mate to tie him up? But now we are really drifting into esoteric territory...
Correction: Harbi will not appear on the second platform if he spawns on the first one. Thus the only requirement for keeping Harbi off the second platform is to keep the last mook on the 1st platform alive long enough to get possessed. After this, Harbi should be eliminated as quickly as possible (to avoid delays in the arrival of the third platform).