I'm not sure I've got a solution, but I've got a preliminary report.
I just played a game where I got to 6% on Turn 870. I'm not sure how well this strategy would play out long term in getting a player to the other UHV conditions, and I haven't tried to replicate it, but here it is. I'd be interested to know if anyone can get the same results or improve upon them.
TL;DR: Build 4 cities (building 2 Settlers); run Culture at 50% (higher earlier, lower later); keep peace with all but one other civ; recruit barbs. Target Simiyan hoton early; conquer Herat and the cities of northern India late. Let the Arabs take the lead in weakening Herat.
More detailed:
1. Set Science to 0% and Culture to 70% and continue to run it at a level that keeps you in deficit. You will have to lower Culture as the game continues—I ended at 40% before crossing the 6% line—and let the deficit go very high if you have to. I constantly kept the deficit at a level that would imply I would run out of cash on or about Turn 30.
2. Send 2 Settlers northwest. One settles Volgograd (but it won't be called that) on the tile between the Don and the Volga, one tile south of an Iron Hill. The other settles a city 5 tiles east and 1 tile north of Volgograd; it is 1 east of a Stone. Send an Orghuz with each as a garrison.
3. Build 2 Settlers in the most Settler-productive cities. (Set the rest of your cities to producing Wealth; always produce Wealth.) There is no really good place for these to build cities, but every little bit helps. I sent them north into southern Siberia -- one on a hill tile that was Historical and one north of the Copper in what was technically Foreign territory -- but there may be better locations for border expansion.
4. Immediately send 4 Orghuz east to conquer Simiyan hoton, the barbarian city east of Beijing. After taking it, leave one Orghuz there and pull the survivors (you will probably lose at least 1 in the assault) and return them west. Disperse these Orghuzes near borders so that they can hit and recruit any barbarians that spawn.
5. Immediately send the Scout west to contact Byzantium.
6. Keep peace with China and Arabs and Koreans; sign open borders with China.
7. As soon as barbs spawn near you, declare war either on Byzantium or Tibet. It doesn't much matter which, just one of the powers that can do little or nothing to hurt you. Use Orghuz to recruit barbarian units. Your choice to declare on Byzantium or Tibet may depend upon how soon barbs spawn.
That took care of the first five or so turns. After that, I collected every barbarian unit I could, watched my borders expand, and kept an eye on my deficit, adjusting the Culture slider as necessary. Around about turn 18 I started watching Herat. The Arabs moved against it around Turn 22. When they had weakened the defenders (but exhausted themselves) I swept down with my army and took it. Then I turned east to invade India, taking Lahore and Delhi, both of which I sacked for my treasury. By Turn 27 I had 6.1% coverage, and that was while both Indian cities were still in resistance. My stability was borderline Unstable by that point, but I hadn't been paying much attention to city management, and by calibrating my populations I might have been able to keep my Expansion stability out of negative territory.
Various notes:
1. Possibly I could have got to 6% by bypassing Herat and taking Bhopal instead. India only defends with Archers and its special Longbowmen, and the latter seem easier to take out than Crossbowmen. Certainly the Archers are.
2. I did not trade for Artisanry so I could produce Culture. But at the end of the trial I gave myself Artisanry, set my cities to producing Culture, and adjusted the sliders to give me the same deficit. In the cities I checked, I produced less Culture than I did by setting the Culture rate high and subsidizing it with Wealth. But this was a rough and rude check.
3. I didn't try pillaging tiles, but China does look to be the best source of these. I would try concentrating Horse Archers in the west to use for conquest, and Orghuz in the east for pillaging China.
4. Looking forward: Simiyan hoton can be taken because it is defended (usually) with an Archer and some Militia. It also counts as a Chinese city for the Silk Road, so I think that taking it means you won't have to go to war against China to get the eastern end of the road.
5. Similarly, I think it might be possible to score a peaceful Mediterranean end to the road. There is a tile in Anatolia, south of the Horse, that was outside both Arab and Byzantine borders on Turn 27, and which is 2 tiles away from any other city.
6. I have no idea how to attract the Silk Road. I improved every Camel, Cotton, and Silk I had, but I hope I don't have to build Weavers or additional Workers to improve the landscape, because Wealth was about the only thing that let me run Culture at the level that got me those borders.
EDIT: Okay, the same strategy with some variations got me to 6% on another game (new start from Main Menu), though I passed 6% in 890, so it's a very close-run thing.
1. I got to 6% by bypassing Herat (which had been captured by the Arabs early on) and taking three cities in India (Lahore, Delhi, and Bhopal). Otherwise, I again built 4 new cities (the 3rd and 4th in slightly different locations) and again I conquered Simiyan hoton early.
2. Culture: Every couple of turns I calculated my cumulative deficit out to Turn 30, and set my culture slider so that I would run out of money on Turn 30. I rounded up, so that my deficit was actually larger in most turns than I could sustain out to 30, because I knew that I'd be getting money from the Indian cities. With 4 new cities built (in the general locations specified) plus the 4 conquered cities, this was enough to let me skate past 6%, as I said, in 890. I didn't sack the Indian cities because I calculated that I didn't need to in order to keep my treasury positive even when running Culture during the last few turns at 100%.
3. Invading India: I suggest taking no fewer than 14 Horse Archers on the campaign; I went in with that many, and came out with 5. Also, if the Arabs take Herat and won't sign an Open Borders agreement (which they wouldn't, even after I converted to Islam), I suggest moving against India (leaving Merv, where you should concentrate your army) no later than Turn 16 in order to get there and make the necessary conquests. This, though, presumes that Sirajis is still Independent so that you can traverse it without a DoW against Arabia.
4. Also, I suggest making peace if possible with your sparring partner (Tibet or Byzantium, likely) before invading India, so that you don't have barbs to worry about, particularly those in India, who will otherwise be an extra threat. At peace, they have to stay outside your borders, though they will attack you if you move into unclaimed territory.
5. You must pillage both India and China to get to 20 tiles. Use Orghuz in China, and do your best to end each turn with your units inside a Chinese city so they can't be attacked. Use a Horse Archer (if you can spare them) to scout out China for corridors you can traverse when moving from city to city. Start a turn in a city, move out to pillage a flat tile, then move back in. Save hill tiles for the very end, when you will have to end your turn outside a city in order to pillage. Regardless, be prepared for the pillaging of China to be a suicide mission. I did this, and I did get 20 tiles, though it was 20 tiles exactly and I'm not sure I could have gotten 21 before the deadline. I'm thinking it best to move a few Orghuz into China early to make easy pillages using Chinese cities as a base.