From the photo it looks like you have just the one "single stage" regulator attached to your Sodastream cylinder? It is impossible to make such a setup hold to a satisfactory pressure for a handpump. You might get low PSIs set for a session, but the pressure will drift way off for the next session. You also have an Angram pump which tend to groan and creak when subjected to even 5PSI (I think it is the pump-cylinder's "flapper" valves vibrating).
A "dual stage" regulator might help but they are very expensive (£70 or so).
I use secondary regulators, setting the single-stage regulator (now the "primary" regulator) to 3-5BAR (40-75PSI) and one of these (click the image for a purchase link):
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You'll need adapters to connect the 1/4" BSP and 3/8" BSP ports to your gas line (easy).
If you don't think 150mbar (2PSI) is enough (it is more than enough!) you can get these
>20-300mbar version< which will go up to 4PSI.