Personally I keg so I brew up the cider, add a couple litres of fresh juice and straight into the kegerator, force carb and serve It's lovely and easy. But that requires both kegging and the ability to chill the keg and keep it chilled.
There are actually a few options for bottling though:
Forced carbonation using the Soda Stream method you discussed- just be aware: wine, beer or juice tends to fizz and foam a lot more than plain water so go slow, do it in the sink and be very careful taking the bottle off the soda stream machine as it WILL foam up quite a lot. (Incidentally, this is also a great way to make your own sparkling wine. Buy a nice bottle of sweeter red or white wine and run it through the Soda Stream!! You want slightly sweeter wine as the carbonation cuts through the sweetness and leaves the wine pretty dry)
For natural carbonation, basically do the old "homemade ginger beer" technique:
Brew the cider up as normal. Follow all of your six steps, just use normal preservative-free juice or fresh juice at step 5. I use the Berri Apple and Pear juice from Coles/Woollies. It's only a few dollars for a 2L container, no added sugar or preservatives, and the pear rounds out the flavour a little bit. You could even use fresh apple juice from the fridge aisle though.
After bottling, leave in the bottle to carbonate for a just a couple of days and then immediately transfer all bottles to the fridge. A few days in the bottle will allow the cider to carb up a bit, and then chilling in the fridge will halt the fermentation and stop it carbing up any further. You'll retain a lot of the sweetness from the juice, but still get fizzy cider.
Couple of caveats:
1) You'll need to keep every bottle permanently chilled till it's drunk - store them out of the fridge and it will start to ferment and continue carbing up and you'll get bottle bombs.
2) It may take a little bit of trial and error to work out how long to leave the bottle carbing. With the old-style ginger beer method, you generally open a bottle every day till it's reached the right level of fizz and then chill them all down.
If you're looking at doing this, I would recommend skipping the normal glass bottle and go with the Coopers style PET bottles. The screw caps make it easy to open a bottle, test its carb level and then reseal it if it needs a little more. Even better, you can squeeze the bottle to feel how firm it is. You can tell pretty easily when it's carbed up that way.
Also, the PET bottles tend to be a little more forgiving than glass if you over carbonate. Glass explodes leaving shards everywhere. The plastic bottles tend to just burst the cap, so you get cider everywhere but no injuries from shrapnel. Pretty sure you can buy a case of empty Coopers bottles from KMart or BigW. They're easy to wash and re-use so if it's going to be a regular thing, they're definitely worth looking at. But you could even re-use Coke bottles if you want to.
Depending on your fridge capacity, it might be worth looking at doing a smaller 5 or 10-litre batch at a time so you have fewer bottles to keep cold. Coopers bottles are 740 ml so a 5l batch will give you 7 bottles and a 10L batch 14 bottles. It's a lot easier to manage smaller quantities in a household fridge.
