Yeah, absolutely no disrespect taken! I do not expect to be running the deck at perfection levels my first time out of the gate - especially when Astra has an uphill battle anyway. My greatest concern is that I do not see the potential for T1 in the deck. When I first played Kith / Cato / Eldorath, it was obvious that even when I lost I was wielding something that had a solid shot at winning. Throughout the day today, I never felt that I could achieve even a 50/50 shot against any of the decks I faced, regardless of tweaking or player skill.
These are all fairly linear decks, at least compared to Coteaz. Each card they play is individually quite strong. By contrast, Coteaz (and a number of Straken decks before him) is fairly combo oriented. There is no card in the deck that's as strong as Librarian or Destructor on its own (closest would be a Snakebite, but it's still behind a lot of top tier 2-drops). The command units are obviously very linear, but most of the combat units and Coteaz usually go off as a combo. It's akin to playing a Power Shutdown CI deck: If you try to play the cards as is, then the deck is going to seem a lot less powerful. Rather than try to win on the merits of individual cards, your aim is to push the opponent into one large combat with a death ball and go off with Preemptive (or draw into Black Ship and just win).
If you jump back to the beginning of this thread and when Coteaz was initially released (around a year ago), you can see similar complaints to the ones that you're voicing now (particularly Federico's post). Since then, people experimented a stumbled upon decks that look like this and this which relied on comboing off with Staging Ground and Preemptive Barrage. Early on, a lot of players didn't respect (or even know) just how much firepower Coteaz can throw down during ranged with a Henchmen and another AM unit. This resulted in a lot of bloodied Warlords and Coteaz able to bully his way to easy wins shortly afterwards. Over time though, players have learnt to respect The Hammer™ and so avoid pushing him, aiming to win the longer game. It was quite possible to push a win on the short game if the flop favoured such a victory, but you were ground out over time. Or so it was from my playtesting experience.
Ammo Depot makes a large difference to the longer, more grindy games, especially if you're forced to operate under the weight of a Palace. The problem with the card is that it can be very finicky about average unit costs, and even with the shortest cost curves, you can still frequently end up with turns where you cannot play down to three cards and the Depots become stuck from that point onward. In Zarathur (and Ku'gath) the card operates amazingly since there is a lot of flexibility in how you spend your resources and you have the possibility to spend cards to help pay for units (SPA and PoG). This is where Ellonellanfair's idea to play Muster comes in since it allows you convert a card into resources in much the same way.
Having tested a previous iteration of the deck, I've still found the Kith matchup a little weak, though not for the same reasons you've expressed. The typical loss would usually arise from longer games (short wins are near impossible) and Kith eventually drawing into Den and auto-winning while I'm unable to keep the Khymera under control as she draws answers for the Mortar Squads. It's not terrible, and drawing Black Ship is much like Kith drawing Den, but on average, it was still a little behind as you lack the unpreventable mass removal of Chaos to really keep the Khymera in check.
The current iteration has a little stronger early game pressure thanks to Transport which makes some difference, though I haven't tested it extensively. The matchup hasn't struck me as bad so far.
Let's say I have a game against Cato and I get 20 cards to Cato's 14 cards. I believe that Cato's 14 cards win the game. The quality of the cards, along with a synergistic strategy, form a deck much greater than the sum of its parts. The 20 cards that I get with Coteaz Swarm are simply the sum of their parts.
This is where I'm going to have to disagree with you quite strongly. Mortar Squads, Coteaz, Markis, Preemptive and fodder are a monstrous deathball that's actually quite difficult to stop. You can get a shocking number of Mortar shots in with the right setup along with a few big swings from Coteaz.
Now take Coteaz. He takes an ability to sacrifice his own units and combines it with - and this is where I get stuck. Sacrificing your own units is inherently disadvantageous. Every unit is invested resources, and usually cards, so these sacrifice abilities have VERY high real costs. The payoff has to be remarkably good. Therefore, Coteaz is only as relevant as the effects that he can utilize, and those effects must be significant. Are they?
Complementary to the combo idea presented above, you also have the idea of trading down a board position. If you've been able to outfarm your opponent, your situation isn't nearly as bad if your sacrificing units that also trade down the opposing board. Card-for-card, you're ahead if you can reduce a board of 10 vs 8 resources to a board of 3 vs 1. The question is manipulating the board situation into one where you can start making that sort of exchange (or better via combo). Triggering one Mortar Squad in a small skirmish isn't going to get you very far. Triggering two in a large pitched battle, and suddenly the sacrifice seems a lot smaller. Similarly, sacrificing a ready unit costs you in future potential, but exhausted units in the HQ train are an excellent resource that should be readily exchanged for opposing ready units.
With all that said, if you want a more linear deck that features Muster, I would recommend that you try this one out. Infantry Platoons are pretty busted and give you a solid early game threat that's difficult to answer at green planets and it definitely doesn't start out behind compared to other decks. I'm not fully convinced Muster is the right call when you can't re-ready during deployment, but it's an interesting idea and I've certainly spammed a lot of units with it.