That certainly clears some things up, and I’ll admit that budgets, nor the builds/exclusive parts themselves really came up in my initial analysis because it just wasn’t really what I was looking at. I was just concerned with the colours as that’s the topic I’ve seen the “what LEGO would have done” phrase thrown around with the most, personally. I don’t expect LEGO to have ever released a canister-sized set with 5 modified torso constructions in place of prefab limbs, with like 2x the part count of the others in the wave - or like you said, utilized illegal techniques or so many new molds… 
We just happen to have a point of reference for their physical appearances now that the majority of the participating community agreed with, so that’s what I used - we don’t yet have that with their colour distribution.
However, a 3/3 split, or even a 2/2/2 one would still mean that 4 characters using only the primary Metru colours, + gold, silver (and gunmetal), in their designs, would need to have unique canister lid colours that weren’t any of the metru colours, gold, or silver, between them, as those were already being used.
As a rule, the colours also need to represent the toy being sold, and you’d even suggested:
Which I already explored in-depth, but as a refresher: Norik and Iruni use metallic silver and gold lids, so Kualus and Pouks couldn’t - meaning 4/6 of the Hagah’s lids/distinguishing colours would not line up with their elemental colour (using the Bohrok and Mata’s use as a guide for that)
As a side note, since you’ve brought it up, I think the reason we got so few new parts/recolours with the official Hagah isn’t too indicative of anything at all. They were two additional sets tacked on to the year as special edition releases to celebrate an important anniversary for the company, and likely had a relatively thin budget and limited parts palette to work with. The fact we even got new and exclusive molds/recolours with them at all is a testament to the lengths LEGO was willing to go to for BIONICLE at the time.
To be blunt; we will likely never know what they would have looked like for sure. I doubt the Toa Hagah were ever planned to be released by LEGO as a full team of 6 like we’ve been used to. For starters, their names we know them by now, “Toa Norik” and “Toa Iruni” were late changes - originally the character designs were supposed to represent “Toa Dume” and “Toa Nidhiki”, respectively, as two standalone figures.
The sheer number of new parts and recolours with each new year/wave is pretty big - who can really say for sure how these guys could have looked if they had an entire wave of sets to themselves?
Just saying that with the precedents set by the Hagah we actually got, the trends in marketing consistent across the entire release history of the franchise, and available colours in LEGO’s palette at the time - both used in BIONICLE in prior years, and prominently in a concurrent theme in 05, in a very similar application, I think that we can get a pretty good idea of “what if…” 
