There are pressure to temp calculators available on the internet.
Here is one at bottom of page.
Crockett Brewing Force Carbonation
Assuming you are going for say 2.4 volumes and your ambient temp of the keg is 70 deg F, it looks like you should be at about 27psi on your gas. Adjust for your actual temp.
Looks like space is a concern for you, but your carbonating would be a lot more efficient if you could cool the kegs down, even maybe in a basement or something. Can save you on CO2 costs.
edit: Actually just noticed you said your temps are about 14C, which is about 57F. If that is correct than your 20psi is about correct. You could bump it a few psi and see if that gets you what you are loking for.
Your CO2 level in the fridge looks a bit low though. Assuming an average temp of say 3 deg C you should still be up around 10psi if you are looking for 2.4 volumes
The type of beer you are drinking, and the length and diameter of dispensing line come into play as well.
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