Perhaps you should recruit an experienced archaeologist in  well
excavation to accompany you in this undertaking.  It is very dangerous if
done improperly.
I am sure if it is only the material culture you wish to retrieve, you
may have other alternatives.  It may be better to leave the well for a
future project that can be better funded.
You can also study  how wells were constructed to better understand your
position at this point in excavations.
 
One last point.
 
What exactly do you hope to with this information?