I bought a sodastream source off Facebook for $40 because my household drinks gin and tonics most nights which has a few issues: all the plastic piling up, 2.25L bottles going flat if we skip a few nights, and having to make extra supermarket trips or buying a bunch of bottles on the weekly shop. So far I've been really disappointed by the economics of it. The carbon dioxide from the standard refills works out at about $0.50 a litre, and the cheapest tonic syrup is at best $8 for the Sodastream branded 500ml, which is $1.50/L on sale, but also in a plastic bottle which is a bit annoying if trying to reduce plastic, all the way up to the Soda Press Organic Tonic syrup at $3.20/L on sale. Oh Bubbles make a syrup that's in the middle price-wise. I've had the Barkers syrup too which I've been making a bit weaker and that's about $1.90/L although I usually make it a bit weaker than their prescribed amount.
So at a minimum it's $2/L, meanwhile at PaknSave I can get the Schweppes standard for about $1.66, or Pams for $1.25.
I know there's adaptors for sale on TradeMe for refilling canisters elsewhere although not sure what that costs but that doesn't really solve the expensive syrup problem.
I looked at SodaStream a while back and came to the same conclusion - it is not actually cheaper.
I don't drink G&T myself, but the preferred Tonic here is actually Countdown's Diet Tonic which is, I believe, $1.30 per 1.5L bottle - seemed to be a little cheaper than SodaStream, but maybe more like 2/3 the price from your calculations (or, to put it the other way, SodaStream is about 50% more expensive).
{Shrug}