Okay in the last game I had there was a definitely over reach on my part taking and holding 9 cities in the Medieval age with a limit of only 4 or 5. So I can confirm the quadratic destabilizing penalty is significant. It scales up pretty fast. Now ... also I couldn't figure out how to 'liberate' my cities on my own. I'm not sure exactly what I thought I was supposed to do but I tried to roll with it. I changed from Ming to Franks in the hopes I could get my influence production to exceed the Influence lost per turn. Which, I was able to do. Are he Ming too good at making influence? Hmm. I digress.

I'm not sure I recommend playing these games through but if there was some people interested in seeing the impact of destabilization from deficits. 

1. Zero stability seems to reduce event chance to zero. I had no 'bad events' trigger for about 40-60 turns despite the patch notes once suggesting that their odds increase at lower stability.
2. AI Alliance preferences may be more based on having a competitive standing army that you don't use to attack them with than trade & agreements?
3. Being influenced made this easier - I'd get science osmosis events and those kept my research from completely stalling.
4. There's no tooltip or prompt to liberate cities when over the limit.
5. Mercenaries are expensive. But I'll still hire them. >.<
6. 'Strained' should be changed to Satisfied.
   
7. Turning off science victory seems mandatory.
8. Does the AI know how to do a Mars victory?

Turn Here is the save from when I made the choice to keep my 9 cities with a 5 city limit & go Ming. Note the dual deficits. :D - might have to eliminate the english.ctr

Turn 76. Note: I did not eliminate the English. 

Here is the save from several turns of playing as the Ming trying to stave off the Influence debt and defend myself from constant rebel sieges (yay for military stars). refocus.ctr 

Turn 106. Still has destabilizing penalty from both debts. I had at least 5 rebellions. I did eventually figure out with help from (HouseofElixir) on Discord how to liberate cities! From there choosing Italians was the best choice. Going French wasn't a bad choice but I if I choose the French reintegrating and absorbing the IP cities wasn't viable. 

In the end I was able to squeeze out a third place win. I was pretty surprised none of the AI couldn't figure out how to finish the game with a mars colony expedition before the game 'ended'.