I just tried it, but mismanaged stability and ended up collapsing at around turn 365, on Monarch/Normal.
I think the main reason for my collapse is researching economics, gaining a negative stability modifier from merchant trade, which pushed me over the edge. Also triggering a GA too early, which otherwise may have helped me at this point. I was at -12 the last time I looked, with -5 from outdated civics.
Expansion stability is not that much of a problem due to the huge historical area summing to huge recent expansion boni. Expanding further can actually help getting more stable. Also UHV #3 requires a lot of cities to get the 10000

.
Regarding UHV #1 I expanded a bit too slowly and ended up having to run the culture slider for a few turns to grab a few needed tiles. I was unwilling to grab the Swahili land, as they were a vassal to the moors who also kept Cordoba and capitulated the Spanish. I ended up settling on the islands close to the coast in the atlantic, a city in Guinea to bypass a cape, controlling most of the coast (including Congo) from there up to the Swahili land, as well as Socotra, parts of modern-day oman, as well as Anuradhapura (trading company). That got me UHV #1. I also grabbed Ziwa to pump units.
Tech-wise I went Cartography - Gunpowder - Exploration - Firearms, while trading for useful stuff. I got Commune, Gunpowder, and a few other, less relevant ones by trade. I timed things such that the trading company finished just after firearms. Trading away my world map as well as a few techs if they could grab enough gold allowed me to run the slider at 100% until around turn 355, where the important techs were in.
From the trading company, paying the gold, I got the spice islands from Java without a fight and went to war over the malay peninsula as well as Anuradhapura, held by the Malays and Dravidians respectively. The attack against the Dravidians was supported by fresh troops from Africa, and I soon went on to the subcontinent itself. At this point, at around turn 350 I had already got around 800

, mostly from capturing cities (Ganga, Anurad, Mascat), but also from pillaging.I already had converted3 cities in Asia to catholicism and had things plannd out to get to 8 in time.
Regarding the gold part of the goal, I feel like it should also include Africa to make it more achievable (or maybe even all historical and conquest area, although that may also make it harder?). Alternatively it could be replaced by something like control 10-12 cities in asia by that turn. Another possibility would be to rework city capture gold to depend more on city size and buildings and less on the time it was held by a certain player.
Unfortunately the dravidians collapsed before I could take more cities, preventing me from getting any more capture gold from them. OTOH this allowed me to quickly grab most of their cities (one going to the mughals), which together with Sumatra would have gotten me 16 trading company resources. I still needed about 6000

from trade routes in 20 turns, but was currently only generating about 230/turn at a bit more than 20 cities. Grabbing a few cities in Brazil, as well as Sumatra should have allowed completing this goal.