-20 loyalty per turn with Victor, and after conquering the original capital and another city sounds like the capital must have moved to another large, nearby city.
Did you keep a unit garrisoned in the conquered cities? Did you buy a monument? Did you chop some food resource to instantly increase the population? Did you establish an internal traderoute with high food yields to grow population quickly? Those things make a difference.
Also, if your target founded a religion (did they?) it will be hard for you to keep their cities loyal without converting them to your religion, which I guess you do not have, having invested everything into your army.
I think we are missing some details from your story, too. If you "stomped your neighbor" (which I interpret as wiping the civ out completely), and their cities still flipped, then they must be under loyalty pressure from yet another nearby civ with huge cities - in which case your conquest must continue.
I figured out how to see the breakdown (like I said, very new to Civ VI). Going down by 16 per turn after Vic and a garrison. Looks like having more amenities would save me 3, and having waited for them to attack first by exploring to meet them earlier and going slinger->builder would have saved me 6 (I just checked a different save on a defensive conquest, and was losing 0 from this). At first I didn't think there were any food resources to harvest, but there are cattle nearby, which seems ideal since you only need Animal Husbandry to harvest them. That would still leave -4 per turn or so, probably enough to buy me some time to take over her other cities and domino. But even then, that would not save this scenario, since it was a surprise war.
Other conclusions I've learned since then:
- T70 is way too late to be starting a WC rush on Epic (most have walls by 2700)
- Barbs will take out on on T20 if you have no slinger. AI will DoW by T30 if you don't have more than a slinger. This can be used to your advantage to "start" a defensive war with a powerful unit 1 turn from comp[letion in store.
- If you're having insurmountable loyalty problems while conquering, rest up for the 4 turns you have loyalty, and move on. After you take out other cities, there will be no pressure from the "Free" cities, allowing you to re-conquer them.
- 2 archers have good enough siege capacity to allow you to take a walled capitol city with your WC, as long as you have 5+ to rotate as they get bombarded (I took out Cyrus with this after reload, with only 3 land tiles around the city)
- Ziggurats rock for spamming in your newly conquered cities. They'll all start with 1 pop, but as you're just starting the classical era, you can work 2 zigs and have +4 science each in the 5 newly conquered cities you have, putting your pace ahead of the AI in order to catch up in the medieval era
- Magnus + harvesting non-triable food resources and rainforest is insaaaaaaane to kickstart a 1-pop city. Seriously 30 turns ahead.