Txurce
Deity
What I currently do is settler spam, grab as much continuous land as possible, keep the satellite city populations low, around 3 or so, send food to the capital, grow it, build infrastructure in the satellites that address happiness, then let them grow when Progress is finished.
Once Progress is done, there's a gold per births mechanic that makes satellite city growth extremely profitable. At that point you could run a loss building a huge army and navy, letting loose your population growth and you'd be running a profit just from the births alone, especially if your cities completed granary and aqueduct before turning off avoid growth.
When playing progress the capital is special and should still be ahead of other cities (this is something I didn't realize at first) so maybe its an issue people are having. I will often get my second city to just 3 or 4 pop and work high production like mines so it produces stuff, including settlers. Sometime I rush towards forge as well, this city often becomes a military or wonder spammer. As odd as it sounds there isn't much need to prioritize growth
If you want to do well with progress I'd try the USA, he is really strong and I'd play him now because I'd say a nerf if probable.
I'm playing with them, and had already settled into a feed the capital and have someone else build the military. (The builder also built 2 early Wonders!) But it's interesting that both you and jma22tb keep growth down. I'll try it next game.
Why do you think America will be nerfed? They're fun, and strong, but don't strike me as OP.