In particular, grabbing Lisbon
Lisbon fell off of the table for us as Joao settled on top of an Iron Resource (Churchill did the same annoying thing, too)--I'm not sure where the AIs settled in other teams' games, but I remember seeing a screenshot of an Oporto being located 1 E of Joao's Iron, which would have made a world of difference, as then one could have declared war, Pillaged the Iron, and had a lot easier approach of dealing with Joao. In the end, we made good use out of Joao by getting him to trade us Machinery and Feudalism due to being Friendly toward us and by having him build The Colossus for us to capture.
Istanbul and marble (for much earlier MoM)
We could have used an earlier MoM, but our plan was because Hatty was trading Stone to Mehmed for Mehmed's Marble, we'd get Mehmed up to Pleased status (at which point he would trade Strategic Resources with us), use Spies to Sabotage all of Hatty's Stone Resources (to cancel the AI-AI Resource trade without Hatty spamming Units when we weren't in a position to go after her Cities), and get Marble in trade from Mehmed. The plan almost worked, as, even though a couple of our Spies failed at their Sabotage Espionage Missions, we stopped that Resource trade between the two AIs, only to find out belatedly that Darius had Culturally stolen Mehmed's second source of Marble. We lost our Scout that would have revealed this fact to us during our first war against Stalin, during which time we efficiently took several of Stalin's Cities. Had our Scout stayed alive, we likely would have sent our navy to the Black Sea sooner (as it was, our southern navy was mostly wandering back and forth, not having a true mission at that point in time due to not having revealed the path from the Mediterranean to the Black Sea) and would have gone to capture Marble from Mehmed proactively by seeing that Mehmed no longer possessed two Marble Resources, so as to get Marble in trade from Darius when Darius' Cultural Borders predictably overtook both Marble Resources, as we ended up doing, but only after a long and protracted second war with Stalin that was in part launched due to wanting to get our war ally of Mehmed up to Pleased status, and also in part launched due to just barely failing to take Moscow in the first war due to some bad luck in Stalin's random Unit-production choices (or, dare I credit an AI and say that it was his brilliant tactics?

).
The Istanbul area was very useful for spamming units for Gandhi and Mao.
It was also a great location for spamming Islamic (Apostolic Palace Religion) Missionaries to the AIs for our Apostolic Palace Victory, although we ended up delaying that plan by whipping other items instead of putting Missionaries as a priority, as we were still focused on an Espionage Cultural Victory, believing that if most AIs gave Stalin-like resistance that Conquest would not have been the fastest Victory Condition for the map, and thereby preferring the predictability of determining the turn on which to win a Cultural Victory rather than the harder-to-predict timing of an Apostolic Palace Victory (of which the timing is still somewhat controllable with some planning, but it becomes harder to predict the timing that far in advance to know exactly when you'd have completed the Railroad and be ready to win).
In any case, TA used HAs to capture Hatty's cities, just the same as Jerusalem, and we also didn't capture them nearly as early as PR.
We used a northern navy and went for London and York, then German coastal Cities, and finally Stalin, eventually getting the wonderful Great Person Farm out of St. Petersburg of which you speak, although we were light on Horse Archers due to simultaneously building The Great Lighthouse and were using a lot of Chariots instead, even at a cost of delaying Granaries just to get enough Units to ensure a guaranteed successful initial attack on London.
Hatty was the only AI really able to help with the team's teching
That part of our game went brilliantly, with us stealing these techs from Hatty:
Code of Laws, Philosophy, Mathematics, Construction, Monarchy, Theology, Calendar, Aesthetics, Civil Service, Literature, Music, Drama, and Nationalism (yay, Drafting and The Taj Mahal).
In hindsight, I'd have like to have captured at least St Pete's and maybe Moscow,
We almost did exactly that, but when we got to the gates of Moscow, Stalin had whipped what we felt was just one too many Spearmen, so we failed to score Moscow in the first war, making for a much tougher challenge. Had it been a whipped Swordsman or Axeman, I think that our game would have played out significantly differently, with us having broken Stalin's back in the first war and possibly not needing a second war, allowing us to go for Mehmed many turns earlier and thus starting our Golden Age chain a lot sooner in the game.
We'd played a game with a very lean army and efficient warring, so we didn't want to risk throwing it all away at the gates of Moscow.
We eventually did take down Moscow in the second war, but at a cost of our army being engaged for about an extra 15 turns against a foe that had a significantly larger army than ours, with the capture of Moscow only happening after we'd pretty much ruined Moscow itself, only really gaining us the full use of St. Petersburg and other nearby ex-Russian Cities.
Drafting of Musketeers definitely bought us our end-game army relatively inexpensively, thereby enabling us to get Feudalism and Machinery in trade from Joao since we didn't need to tech Guilds early on, and gave us the rough equivalent of Knights (a bit weaker overall, but no intrinsic weakness to Spearmen/Pikemen).
Going for Education allowed us to tech Liberalism for Railroad, thereby saving us Flasks even with having to tech 2 extra techs, and we built a 1-turn Oxford, but we hadn't been proactively planning our building of Universities and I don't think that we started that planning until we were one turn away from learning Education, so I think that we spent 11 turns building our Universities.
Yes, I do believe that if taking down Hatty had been as hard as it had been to take down some of the other AIs, there would have been a much more significant initial investment to take her on, making for more comparable games to teams that went for other AIs, with the cost not only being having to self-tech the techs that Hatty would have otherwise teched but also losing early-game Units, rather than the opposite effect of getting easier Promotions for veteran troops on top of easy Wonder captures for only really the cost of having to self-tech more techs.
We also had to struggle hard to get our second Great Person for our first Golden Age, which would have come naturally without much effort just by owning Alexandria with The Great Library.
Sure, we read the map wrong and didn't believe that Hatty would be so easy to take on, really believing that she'd have an army of Archers, Spearmen, and War Chariots in high Cultural Defence Cities, which wouldn't have made sense for our rag-tag army to take on given that we were also building The Great Lighthouse. The Jerusalem lure for spare AI Units built by southern AIs (including Hatty) clearly worked in favour of the teams who went for the southern AIs early--there was no such AI-Unit siphon for Russia's Units.
We also underestimated the cost of an Espionage Cultural Victory, so we dumped far too many resources into that failed endeavour, and while we built a ton of Spies, we didn't use them effectively for Support City Revolt Missions after the first one failed at very high odds of success.
The top-ranking teams played excellent games and I am truly happy for their successes; the map was great and was one of the better SGOTM maps; that said, I think that it could have been an even better map with a more-challenging Hatty, forcing teams to pay a high investment cost to get the large benefits that came from owning her Cities early on.