I opened the file this morning before going to work, too curious to pass it up. That battle went really well for me, 2 dragonships and a galleon vs 2 dragonships, 1 frog and 2 lizard archers should be closer. Having first shot matters though. Still, I expected to lose the fleet, I moved it there by mistake - I wanted to first gather up 5-6 lizardmen more that I had a bit north of there.
1. On the RP: yes it's fun, but it's not so far from the truth, don't forget that to welcome this noob the goblins razed my farms on turn 5 or so ;) Agreed on the goblin rp!

2. Azracs are not as powerful as it seems in this map. They can gather an enormous empire by farmer's gambit but it's indefensible, there are teleporters landing on the NW surface corner (orcs), NE cavern just below the capital (goblins), and centre-north border in the caverns close to a gate to the surface (from the teleporter in the SW close to the halfling/lizard border, not so difficult to access for lizards or dwarves). I suspect that what you saw as initial advantage is rather coming from the higher starting gold, but that matters less. They're also the ones that need most time to reach the deep, it's quite surprising that I ended up possessing most of it. I've tried the whole match to reach the goblin teleporter just to be beaten to it by the orcs when the goblins committed harakiri after blocking me for 5? turns, till I managed to come out with a digger. I didn't expect you to end your mana so quickly, now I am at 1 turn from casting mana leak.. I'm already in the negative with all the godl rush I've cast, but I have something like 3.5k in the vault. I think you would be a giant pain if you didn't abandon ship, you've underestimated how much it takes to get to your capital... To entertain you: your balloon in the north after becoming independent has conquered another undefended dwarven city on its own, it's painful that troops are built at the end of the turn of the independents! Makes life easier for the last one.
Another funny bit: I had a flying galley trying to transport my stacks of mixed archers from the area surrounded by lava that I took from the goblins, but it couldn't because of your damn balloon full of fire-halo'd bombardiers! I've had easy time dealing with it now as independents and they've still managed to pop my demon. The demon hasn't made a single casualty in its brief time in this dimension. Oh, and I "lowered terrain" in the mountains close to the 2 caves that bring the dwarves to the surface, so I was closer to attack your rearlines than you realised, but Ham was around there and with some archers he would have easily repelled that. My last line of attack was the driller that was tunnelling towards the farms to the east of your capital, 1-2 turns for an airship to do so on the other side of the river.

3.On warp party: in Eve Online there was a saying, what helps the solo helps the blob relatively more. Or, whatever tools the underdog can use to fight the higher force, the empire can exploit more. Warp party doesn't differ. If you're using it to menace me at 19/9 hexes from a city that you conquer, I can do the same but those hexes represent a much higher percentage of your lands. OTOH, I saw your post about 19/9 hexes only after my previous comment so I consider it less problematic now, but make no mistake: it's more a tool to win harder not to resist the winning party. In this case you had more casters which matters, but usually I'd expect a snowballing player to have the advantage - either heroes or mana...
On the other hand, I think you converted the elven 4 square city, that's unattackable, and with a small node it's the perfect place to warp party in my rearlines on the surface. The only defence against that that I could think of is mana leak.

I don't think there's a balance problem. As long, that is, as all the players realise what this map entails: a race to the giant vault. That's where the fight takes place, because owning it makes it pointless to fight for the other nodes, invest in fixing the teleporters that bring to the 4-node corners in the deep, and owning more than the cities that can send quickly reinforcements to the vault. So, the advantage goes to goblins and dwarves, which are the closest to start from the teleporters. But it doesn't matter that much normally each player should reach their deep city before it's conquered - apart perhaps azrac, if the dwarves go for their city immediately after entering, it's pretty close. Air magic rules in a race, and if someone's lucky enough to start with haste that's even better. This then compounds with the magic item list which makes summon hero doubly powerful: you can qickly build an unbeatable taskforce, no need to level them if they can get +5 in all attributes with objects.

So if not balance, what's the problem? Well, if all the players realise that this is about the race, then this beautiful carefully crafted map becomes less and less relevant the farther away you go from the 4-square cities and the teleporters to the deep, quickly reaching irrelevance. I'd play azracs much differently now. I would say that this is what needs to be fixed.