One thing I could use some advice on: as I mentioned before concerning my hypermobility, I struggle with my very hypermobil shoulders. They're very unstable,  which makes coming out of any push-up style move incredibly difficult.   While I can easily go down into chaturanga, coming back up doesn't happen much for me.  I'd like to know if there's anyway to train, safely,  so my shoulders can be more stabilised making the up part of a pushup/chaturanga more possible? Thanks.  

1) do push-ups at an angle where you can confidently push out of the move. Leaning against a counter for example. 

2) I am a big fan of weight training. Shoulder work in all planes of motion is a great way to build strength and safety. 

3) You can practice chaturanga with a bolster (or 2) under your upper thighs to take the weight of the lower body out of the equation. 

Hope that helps!