Hi Willofig,
I would wait until July. Those thick stems are energy reserves.
So wait and if you have the choice between root shoots and leaves popping on the stems, keep the ones on the stems.
Of course, those stems could be toast and by July if nothing is popping than you can expect them to be toast.
We are still in May, so it is too soon to be sure.
In 2011, I began removing some branches until I just knew I shouldn't have removed the last one... But of course it was too late . So I stopped and let the tree have more time to recover.
On a branch that remained, I got some 8 figs and nothing else from the tree that year . So I always think that with more patience, I would have 8 more ... So now I'm patient .