@Minou
For end game planning for SV I feel like there is 2 big scenario : One where you focus on culture to reach Democracy/Globalization, and one where you just try to push science as hard as you can.
If you have good culture you won't need more than 2 spaceports(bought with Reyna). The first one will be used to launch Satellite, Moon landing, Mars colony, Exoplanet expedition with Royal society and Pingala established with the 3rd promo. You can put 1 or 2 chops in the Exoplanet expedition but just try to save your chops for Lasers projects.
When you discover the techs allowing you to launch Lagrange and Terrestrial laser you can start chopping both cities at the same time(one with Pingala, the other with Magnus). While you are chopping projects make sure your cities are powered, you need A LOT of charges to chops and improve the city with Solar and Wind farms.
Before buying your spaceports you should be planning on getting Big ben and enough treasury to buy 2 spaceports, 2 encampements+buildings, tiles(you need a lof of money for tiles) and if you are planning on getting Amundsen-Scott uni+techlab.
If your science is very strong but have poor culture you might need to go with 3 spaceports, the first one will chop Satellite and Moon landing with Magnus to reach T3 governement and Royal society so you can boost with 7 charges builders the Mars colony and Exoplanet expedition projects and chop Lasers.
The first spaceport city need just enough chops for Satellite and Moon landing and don't need an encampement. Be careful with your governor titles because you will need the 3rd promotion of Reyna earlier and the Royal society come after the first spaceport.
You can't delay Big ben to grow a bigger treasury because you need the first spaceport very fast. If you are low on money you can build Eiffel tower and use Neighborhoods gold to buy the 2 lasts spaceports/tiles/etc... but it require some planning and builders charges at a time where builders are already very expensive.
Amundsen-Scott will come too late to be useful in this scenario I think and is too costy.
Some advices:
You don't need productive spaceports cities but lot of trees.
Make sure to save 2/3 chops in your governement plaza city for Royal society.
Consider getting Bolshoi Theatre and Oxford University, very nice wonders for SV.
Don't forget to established Liang close to your spaceport city for 7 charges builders.
3rd promo on Moksha can be very good if you want to buy a campus with faith near snow(for Amundsen) while Reyna buy spaceports.
Start saving your low charges builders when starting to plan the Big ben city. (don't forget to chop crabs/copper before Big ben)
You can buy a settler with faith to chop even more workers near your spaceports cities if you need more workforce.
You need
A LOT of charges to chop and keep you spaceports cities powered!
Timing may vary a little depending on map/city-states/civs etc....
4/5 spaceports seems unreasonable.
How was your experience, did you put a lot of turns into future tech or was your science barely enough to get you all the relevant techs when you needed them?
I don't recall everything on this game but I won the game 4/5 turns after launching the Exoplanet expedition.
You really don't have to worry too much about production. The new bottleneck I would say is how many builders charges you were able to save for the last phase.
Tech lab is a good investment but you have to power up the city to make full use of it's bonus or reach T4 governement.