England's tricky because you really start at a disadvantage compared to your neighbors and must be very efficient at conquering Scotland and Ireland. Scotland is very well defended, but I've had good results getting the conquering Norse to gift Edinburg thanks to pressure from a Republic Artist culture bomb or two. Ireland can be taken with a couple of Lancers, though bad rolls mean it's worth having them in excess. Otherwise Beelining the National College is essential.
For the first UHV, South/Central American cities are a priority since there's not a lot of space and the Europeans are gonna swarm there very quickly - Aztec conquerors can take a city in Honduras or so, then there's the Caribbean, Florida or Guyana. North America can be delayed outside of two or three cities in prime spots which can build troops. Africa I delayed too much and had to conquer the Swahilis at the last minute. The 25 naval units is a deceptively simple goal that still requires a decent investment in

. Colonialism is your friend but you'll be short 1XP - this can be obtained with Drydocks or an early Trafalgar Square, but a Great General is much better since you can get it early. 4XP Privateers can get the fifth point with relative security along with filling the Great General bar. It's best to have two or three dedicated cities on it to be sure to get there in time.
On Regent/Normal, I didn't find the tech UHV to be a problem, though quick colonization can kill your maintenance, so you're right that the two goals are in opposition.
I haven't done the last UHV yet, but at this point I think the strategy is to flood India and East Africa with your technologically advanced troops and workers/labourers (it's a bit of a hassle building and transporting them though, but at that point you don't need to build much else). One issue I have is that the Ottomans control Egypt and are the top player, so I'll probably not bother fighting them and try reaching the Mediterranean coast through settling the desert.