The trick to have well carbonated beverages if all you have available is a sodastream-like device:

- cook the water to remove any other disolved gasses

- Cool it down to as cold as you can. A sludge of ice and water is very close to zero °C

- keep some ice unmelted

- carbonate

This is a bit annoying to do especially step one (I skip it, it seems to help bit not to a huge degree) but it helps making very carbonated water to mix with the sirup

Nice, I will have to try that!