Link's got some good concerns, but I think testing this card is probably the best way to see how broken it is compared to, say, Eye of Ugin. While we wait to see if this card is broken, let me suggest an even more ridiculous card to pair this up with: Palinchron.
What about a rider that says "Whenever a creature cast for its evoke cost dies, exile it"? That should eliminate the reanimation shenanigans. Also, boosting the evoke cost to may be necessary.
Might not be clearer. Those players might think they can pay the mana cost, and the alternative cost to cast their creature. There are a number of cards where you'd be willing to still do this, including the evoke cards that trigger on going to graveyard, like Reveillark.
With the big Eldrazi, this becomes a bit crazy. Ulamog becomes UU: Destroy target permanent and shuffle your graveyard into your library, Kozilek draws four cards, and Emrakul gives you an extra turn. I just don't know if this should be made, even at 7 mana, because there are so many potentially broken combos. If you have Adarkar Valkyrie or Cauldron of Souls, for example, all of your creatures suddenly cost only UU.
Check evoke's reminder text. The creature's controller sacrifices it (not "you").
Hmm, 1/1, 2/2, 3/9. Nice!
Rally is now "other" by default.
Hahahaha. Yes. But the brokenness there is definitely on Palinchron's side :P
Link's got some good concerns, but I think testing this card is probably the best way to see how broken it is compared to, say, Eye of Ugin. While we wait to see if this card is broken, let me suggest an even more ridiculous card to pair this up with: Palinchron.
The exile suggestion may be sensible, but I think boosting the evoke cost removes a lot of the fun.
That's quite a sensible suggestion.
What about a rider that says "Whenever a creature cast for its evoke cost dies, exile it"? That should eliminate the reanimation shenanigans. Also, boosting the evoke cost to

may be necessary.
That last ability is a bit crazy. Maybe if other soldiers were indestructible?
fixed typo
Damnation was already very good. Try

for the evoke cost. Other than that, very cool.
Might not be clearer. Those players might think they can pay the mana cost, and the alternative cost to cast their creature. There are a number of cards where you'd be willing to still do this, including the evoke cards that trigger on going to graveyard, like Reveillark.
I think clearer wording might be something like, "Players cannot cast creature spells without paying their mana cost."
Damnation with a body? Hmmm. Nice.
The "as you cast" ones are sensible. I don't know why I never thought of that approach when I was proposing "Splice onto creature".
fixed augment cost
Things like Modular might work - there are "reminder" counters, as it were.
Other mechanics like Flying are going to need something like "~ ETBs with a flight counter on it and has flying"
Looking through the rules, some mechanics that will work easily with Augment are:
Amplify Affinity Sunburst Convoke Ripple Split Second Delve Prowl Devour Cascade
Just testing out what mechanics could go well with Augment
With the big Eldrazi, this becomes a bit crazy. Ulamog becomes UU: Destroy target permanent and shuffle your graveyard into your library, Kozilek draws four cards, and Emrakul gives you an extra turn. I just don't know if this should be made, even at 7 mana, because there are so many potentially broken combos. If you have Adarkar Valkyrie or Cauldron of Souls, for example, all of your creatures suddenly cost only UU.