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In postgame discussions, it became clear that a approach of gold tiles generally beat going for max food. Along with that came up a discussion of how powerful a city might become if it intentionally took tiles that violate the initial variant restrictions. I had to take a shot at that. (I wouldn't mock the rules in an actual competitive game like that, but it sounds like neat material for a just-for-fun shadow.)

I decided to take two illegal tiles. One won't be that much different from an uncheated game. More than two would be too much of a score penalty to have any chance of overcoming. The -5 score penalty applies just once per tile, so we can stack up as many illegal features as we want on that tile. The best possible tile I can think of breaks down like this: lake oasis gold mine with railroad. (Can't add forest. Oasis and floodplains and forest and jungle are all mutually exclusive. Of them, oasis is obviously the strongest.)

2-0-2 Lake
3-0-2 Oasis
0-0-1 Gold
0-1-6 Gold mine
0-1-0 Railroad on mine
1-0-0 Lighthouse
6-2-11 productivity, all on turn zero except the lighthouse food. Moai Statues can add a hammer, but I intend to skip that in favor of Ironworks, since not going with many water tiles. Colossus can add a commerce, but only for a small fraction of the game. As a bonus for putting all this on water, the mine can't be spy-sabotaged. Oasis tiles cannot be improved by workers, so if this tile were on land and the mine got sabotaged, it would be lost forever.

The second illegal tile will be the same, except saltwater coast, not lake. I do this because we still need two saltwater tiles for coastal access to qualify for the lighthouse. The only useful thing to put on those two saltwater tiles is regular seafood resources. But the illegal lakes already make for +10 food total including the city center, and adding two seafood to that will be overkill. As a bonus for putting these on water, the mine can't be spy-sabotaged. Oasis tiles cannot be improved by workers, so if this tile were on the land and the mine got sabotaged, it would be lost forever.

As for the rest of the tiles: all gold except for one gems, one silver, and one iron for the Ironworks. I do now feel that the happy from the precious metals pre-Globe is worth the slightly lesser commerce long term. Forest on everything except one of each happy resource; growing on the illegal food, we will need to get them mined ASAP.

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Here is the plan.

1. Work boat while growing to size 2 (pick up the second illegal tile ASAP) and researching Mining.
2. Two workers at size 2 while researching Bronze.
3. Research to Writing as fast as possible while mining the happy resources. Prebuild police warriors now.
4. Mathematics to get full valued chops. (The first two went into the library pre-Math.)
5. Run scientists as soon as the library is complete, allowing growth to slow while the workers improve more tiles.
6. Research to Priesthood, while the workers do the combined mine+chop maneuver, to time two chops into the Oracle.
7. Oracle - Civil Service.
8. Use Hed Rule for happy until we can get the Globe done.
9. Oxford and straight on to Alpha Centauri.

Amusingly, the railroad on the sea gold worked to speed the work boat's movement over to the fish tile. :) And more seriously for all future boats, like privateers.

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Here is the library completing on T25 3000 BC. (There is nothing to do with the overflow beside prebuild more police warriors.)

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Academy on T35 2600 BC.

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Oracle chopped and CoL finished on T37 2520 BC.

Regoarrarr was right: for this challenge, forget the Pyramids. Just research Monarchy and use Hed Rule for happiness. You'll make it to Constitution by the time you have any significant number of specialists. Since it was only two more turns to Monarchy, I waited on Bureaucracy to double-up the Hed Rule and Bureau civic switch. Also, if we are skipping the Pyramids, then stone on the city center was probably the worse choice. I think Oxford is the only thing that it speeds. Marble for the Oracle, Nat Epic, and Taj Mahal would indeed have been better.

Chop overflow into the Confucian Monastery - yes it's worthwhile for more science.

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One turn granary with a Bureaucracy chop. One turn Aesthetics with overflow from Wheel-Pottery. Happy cap at 15 with six police warriors. Sailing for the lighthouse, Drama, then straight to Oxford.

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T59 1640 BC: Globe done, Education in one turn ago. I did slip in the forge before university and Oxford. Health is becoming a problem, but now I can trade away all the happy resources for health.

T72 1120 BC: Oxford done. 700 beakers/turn. The next target to beeline was Astronomy for the observatory, built the harbor while waiting for Astro.

T77 950 BC: Got the Music Artist. Held on to him for a few turns until I could reach Constitution by the end of the golden age. The GA let me adopt Buddhism as a state religion and take all of Representation, Caste, and Pacifism. 3 turns of anarchy total saved.

Great Person #2 is the Oracle's Prophet at T76 975 BC. Settled him for the hammers, cash helps a bit against civic upkeep, and future Rep beakers. GP #3 an artist at low odds, just settled.
GP #4 Scientist in 175 BC (actually low odds, Oxford was the only scientist source), settled.
Physics Scientist 150 BC settled

Sent out Privateers to make contact, which they did circa 400 BC. (Yes, hidden nationality units can make contact.)

National Park done in 150 BC.

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At 1 AD, I have 929 beakers, National Park done, Taj Mahal built to one turn from completion (saving it until I will reach Free Market by the end of the Golden Age.) 1 turn from Electricity on the way to Liberalizing Superconductors. 7 Privateers on the seas. Producing Great People at a moderate though acceptable rate. Hoping for an Engineer eventually for Mining Inc and +17 hammers.

The religions created lovefests on each continent. Hinduism was the only religion on the far side. I had founded Confucianism and Taoism myself, but not spread them. My continent was a lovefest of Isabella's Buddhism. I actually instigated that: I spread the missionaries to convert Sury and Shaka, just in the interest of avoiding war and playing quickly.

At this writing, I'm going to be away from Civ over the holiday weekend, so the game will pause here for the moment. I haven't decided what to do next. Part of me wants to push a warring approach to go for what would be the highest scenario score, but I'm not sure I have the drive to actually push through with that. More likely I'll simply play for a peaceful fast finish and let the score fall where it may.