The natural carbonation thing confuses the issue. Pretend it doest exist for a minute OK
There are two pressures you need to worry about in a keg, they serve two different purposes.
The simplest to consider is dispensing pressure, this is just how much force is behind the beer as it comes shooting out your tap, a reasonable amount of pressure for the amount of beer line you have, gives a sensible pour... too much pressure or too little length of beer line and it shoots out of there as mainly foam. You just need to juggle between length of beer line and pressure till it works for you.
The other pressure factor is related to carbonation. C02 dissolves into water (or beer) at a certain level which is dependent on a combination of pressure and temperature. Its usually expressed as "volumes" of dissolved C02. So if you dissolve 1 litre of C02 into one litre of water, you get 1 "volume" of C02. So when someone says an english ale is carbonated at 1.5-2 volumes... thats what they are talking about, the amount of C02 in solution. If a Hefeweizen is carbonated at 4 volumes, thats twice as much C02 in every litre.
Now, you can force as much C02 into a water solution as you like.... all you have to do is put the pressure of gas up high enough and the C02 will dissolve into the liquid at the gas liquid boundary. But how the C02 dissolves is also dependent on temperature... the colder it is, the easier the liquid holds the gas in solution. Eventually, if the pressure and the temperature stay the same, the system will come to equilibrium, and no more C02 will dissolve unless you increase the pressure or decrease the temperature.
So.... if you make your beer cold... you need to apply less gas pressure to get a given amount of C02 to dissolve into the beer. If its warmer, you need more pressure to get the same amount dissolved.
Now it turns out that at around the temperature of your average beer fridge (lets call it 4C) the amount of pressure you need to get a nice average carbonation for an ale or a lager(2.5 volumes), is about 12psi.... so there is no problem at all with one of the party kegs. They hold 12psi easily. For a Hefe at 4 volumes at 4C the pressure needed is 27psi... so thats right on teh border that the kegs normally hold before the pressure relief goes off. If yours is holding 37psi, you are there easily.
So, inherently, there is no problem at all with carbonating one of these things right up to and including the really fizzy wheats and belgians... you would need to drop the pressure right back when you served them or it would come out at 100mph and you would have nothing but foam... but you could cut the pressure on the night and the beer isn't going to the go flat in any great hurry. you would get through your party no worries.
All clear and all good so far? ..... OK, now comes the bit that makes it not work so well. Lets say you do want to naturally carbonate rather than force it. It should be all good shouldn't it?? The keg holds plenty of pressure for the job right? Well yes it does -
at 4C but if you are naturally carbonating, things aren't going to be at 4C, If the yeast is going to work to carbonate your beer, they are going to be a LOT warmer. So much warmer, that you wont be able to get all the C02 you need in your beer, to dissolve at pressures less than the safety relief valve trigger. Lets try an example:
You have a nice lager that you'd like to carbonate to 3 volumes of C02. You have primed your keg and you are going to leave it in your spare room at a nice constant 17C to carb up. So whats going to happen?
At 17C you need 31.9 psi to get 3 volumes of C02 to dissolve in beer...
your keg is OK, but the average one started to vent gas at 25psi - and thats only enough pressure (at 17) to carbonate to about 2.5Volumes. any extra gas the yeast produces doesn't go into making beer fizzy.... it just goes out the relief valve. If by chance on Tuesday afternoon the temperature goes up to 19, then any gas over 2.4 is out of there ... and so on. At 17C you would need to have 50psi to get a 4 volume hefe carbed up. And nobodies plastic keg is holding 50psi in.
You could do it.... use a lager yeast and condition your beer at 10C, your keg at 37psi would hold in 4 volumes, but most wouldn't get better than 3 ish even at that low temp. And re-pitching lager yeast just to get your beer fizzy is a bit of a pain.
You could, as you said, naturally carb the beer as far as it would go, then chill it down to 4C and just top up the fizz with your sodastream. That would work just fine. But extra sugar for priming wont help at all; you could put a whole other kg of sugar in there for priming, and its not going to do a damn thing to the carbonation... just a bit of extra C02 for the greenhouse and really strong beer
For my effort to reward satisfaction levels, I'd just force carb the whole damn thing with the soda stream. Set it to the right pressure for the carbonation level you want, and shake the crap out of it till gas stops coming through your regulator. No more C02 is dissolving and so it has reached equilibrium and its done. Then when you want to serve it, just dial the pressure back till it pours well.
Hope that makes a bit of sense and helps clarify a couple of things for you. If not - sorry, I gave it a go.
Cheers
Thirsty
