I'm afraid not! That's all hardcoded and it would be a massive change to make it moddable. Sorry!
Based on some reasoning, I've got this list:
Vanguard = Kinetic/Laser, as you said
Dvar = Kinetic/Explosive, also as you said
Kir'Ko = Psionic/Biochemical, ^
Amazon = Laser/Biochemical, putting in Biochemical due to their genetics knowledge
Assembly = Arc/Kinetic, Kinetic as you said, and I'm presuming some race needs to be Arc, and a race of machines could work, even if they might also have a weakness to it
Syndicate = Psionic/Arc, two psionic races, so that's why they have that, and it gives a second place for Arc in the lineup
One Explosive, since you mentioned only Dvar had it as a primary, and three Kinetic based on the provided list, making sure the rest of them were represented twice. Seems like a reasonable guess of the setups.
So, how linked are the terms "damage channel" and "weapon tech," since as we've seen a damage type of 'Thermal,' but no direct weapon tech? Several weapons which would obviously fall under the category of Laser have been listed as dealing Thermal damage, but the Phoenix Walker most certainly isn't utilizing lasers to deal its Thermal type damage.
Likewise, is there still a chance for what I suppose might be called "Cryo" damage to show up? Most of the weapon techs have fairly direct analogs:
Kinetic = Physical
Psionic = Spirit, sort of
Biochemical = Blight(acid/poison), but can technically induce effects similar to fire and shock
Laser = Fire
Arc = Shock
Explosive = ...Fire/Physical?
Cryo damage was kicked out early due to it not really fitting with the Sci-fi setting. It might still come back I guess..
The damage channels were added very early in development of AoW3, when we weren't thinking just getting off the ground and it never occurred to me that they would need ot be mod friendly.
The real question, since we haven't seen any yet, would be the viability of multi-channel attacks. Something like D1+D2 = (I[1] x 0.9^R) + (I[2] x 0.9^R), where R is variable based on the damage type received. It doesn't seem unlikely, since the math isn't any more difficult to parse through the formula, just doing two values at a time. You may be avoiding it for whatever reason, but I'm guessing it just hasn't been shown yet on the very small set of units we've seen.
Planetfall is heavily based on AoW3 code, and the damage channel stuff is still mostly the same system as it was before. I didn't rewrite it because, to be frank, I'd forgotten that people wanted them to be moddable.