TLDR version:
Instead of altering the global culture rate as you gain or lose cities, the same gameplay effect can be achieved by altering the amount of culture needed for the next policy and making that change depend on how far you have progressed towards that next policy.
Note in this post I use

and

to distinguish two different formulas.
(EDIT... Hmm it probably wasn't necessary in the end, but it makes the post more fun so what the heck.
)
f you build that new city 5 turns into your current policy, you're priced as if you had that new city from the 1st turn into your current policy. How is that fair?
Good question, and it has helped make your idea 'click' to me. No matter the implementation, I see now that what you're essentially trying to do is smooth out the discretization of this game mechanic.
A comparison can be made to how combat worked in civ4. Two units of equal hitpoints and strength had 50% odds when facing off against each other, but if one of them had 99hp instead of 100, the odds change drastically. These 'jump points' had interesting consequences, one being that the effect of promotions (like combat I) were not very intuitive or obvious.
You want adding extra cities to be a rate-altering effect rather than a threshold-altering effect. It reduces the micromanagement in waiting for the various jump points (when cities are founded or lost).
A thing to note is that this effect is possible to achieve in a system where you alter the thresholds rather than the rates with additional or lost cities. (explained later below)
Let me give an example. Suppose (using your sort of system) you want your culture rate to be multiplied by 0.75 for having two cities, where it would have been 1.0 if you had only one city. i.e. 25% penalty. Suppose also that you're currently generating 1

per turn and the next policy is at 10

.
Build the 2nd city on turn x (between 0 and 10) and you would have to generate x + (10-x)/0.75 culture to get the policy.
Note that this slightly resembles a 'weighted average' calculation. To be clear, rewrite it as:
1.0 * x + (4/3) * (10-x).
The earlier you build the 2nd city (the smaller x is), the larger the weight you give to the slower rate (3/4 or 75% rate) and the smaller the weight you give to the 1.0 (original) rate.
If this is significantly different to the sort of mechanics you're talking about let me know because this is how I'm understanding it.
Notice I said earlier in this post that it's possible to achieve the same effect with altering the thresholds. Maybe it's obvious, but if not I'll try to do this for the same example presented just a moment ago.
So once again we have our next policy taking 10 culture and currently generating 1 per turn. Build 2nd city once you have accumulated x culture (so it is turn number x again).
To produce the same effect as the rate-change by doing a threshold-change instead, and assuming we don't want to instantaneously change the current amount of culture put towards the policy (i.e. we won't just 'cheat'), then we just need to change the threshold to:
x + (10-x) / 0.75

(i.e. it's essentially the same thing)
Basically with this change it would make the culture threshold bump up by a smaller amount if you are close to the next policy. If you
lost a city, the threshold would be reduced in basically the same way (reduced by a smaller amount if you are near to the next policy). Rather than having global culture rate vary up and down as we gain and lose cities (respectively), we'd have culture threshold vary instead but using the fairer formula than the existing game.
Now what is left to argue is which feels more intuitive or looks nicer (changing the rate at turn x

or changing the threshold at turn x

). Personally I feel that neither of them is clearly better than the other, but the latter

w00t

stays closer to resembling the current system and achieves the same positive effect as what you desire (just using a different way to look at the numbers).