I think there were a number of factors going on. The most important was the order of targets. We hit India first, not Persia. This was important for more reasons than just because Persia had immortals and India didn't, although I for one didn't fully recognize that at the time.
India was the first civ we contacted. They were in war mode from the get-go and had used up their unit support on archers, spears and warriors from long before they could build swords outright. They never had much cash, so that's mainly what we faced -- archers, spears and warriors. In your case, you met Persia fairly late, when they could already build immortals, so that's what they stocked up on.
Second: Keath did face a respectable number of units in taking on India, but relatively few of them were offensive units. Besides the war-timing factor I just mentioned, India had also been dropping off a steady stream of attackers on our territory since about 950 BC, so the attackers on their home island were constantly being depleted. I just skimmed through your thread, and failed to see mention of a single Persian landing on your territory prior to your invasion. (Possibly I missed one or two.) So all the Immortals were still home and waiting for you. I'm not sure why Persia failed to build many boats, but it didn't work in your favor.
As for later in the game, by the time we got to their landmass, Persia had been suffering war weariness for a fair amount of time from all the Immortals we'd picked off at AI Bait. They'd also been living with the lowered unit support of Republic for a fair amount of time. They'd lost access to two luxes when India and Zululand fell and would shortly lose a third. In short, you got them at the height of their power (as we got India, but with compensating factors); we got them when they were broke and hurting.
And of course, you had to fight through their golden age.
I've been looking through some of the other threads trying to tease out decisive factors. The biggest, I think, was the timing of our golden age, which quite honestly I don't think we could have managed any better if we'd hired all the geniuses in the world to plan it out ahead of time. Sheer serendipity for it to work out so perfectly.
Of the factors more under our control, I found two that I think made a difference. First, our consistent use of a bait town. We're the only team of those I've looked at in any detail so far (you, XTeam, Wacken) that never faced attacks in places we didn't want them to come. By leaving the town AI Bait open at all times and never leaving another town empty until the game was fully in our control, we never had to split our forces. Nobody ever landed in India except us, nobody ever landed in Zululand except us, and by the time we were in Arabia, it didn't matter.
Second, the Forbidden Palace. We finished that in 510 BC, about 25 turns before you or Wacken had one, and you were the next two after us as far as I've seen (having checked about a half-dozen team threads on that count). Our whole city setup was predicated on having a FP in a particular town, and although our production suffered slightly relative to strict RCP rings before it was built, afterward, it was fantastic -- we had I think nine towns at minimal or first-ring corruption even before gaining three more with the invasions, without much cramping even.
Renata
and to Keath especially for some very good RL news! 
(You could have taken a bit more time ... it was nice to be the leader for a few days 
)
!
![[party]](/images/smilies/partytime.gif "Party [party]")
It's a girl!!! 
