Well you cant always double the verb for emphasis It works with γρηγορα γρηγορα but it is rearly used like that in everyday speach. It is often used as a way to indicate to someone to hurry
"Πηγαινε γρηγορα γρηγορα" Go imediately
It also works with αργα αργα, slowly Ακρη ακρη, at the side
Διπλα διπλα side by side
And at some other phrases that you should be able to understand for the context. Just do go and double every verb because it may not always be correct
I think there may be an issue with the sentence here. Σιγά σιγά indeed means very slowly and σιγά can mean slowly, but σιγά on its own it can mean quietly as well. So, in order to avoid confusion and make it more clear, maybe it would be more appropriate to use the adverb "αργά"? I understand that αργά also has the meaning of "late" but I don't thing that it would cause any ambiguity here.
I was recently told by a native Greek speaker that αργά would be the better choice in a sentence like this. She said σιγά σιγά doesn't sound good here. I got the impression that σιγά σιγά is best used separately in a command, i.e.: Slowly! What do the native speakers here think?