I'm a bit out of my depth here re free forming. However, if one is not fussy about the exact shape of the top edge (which is clearly the case), there is no reason why a mould could not be used as a body (ref. my moulds posting) with a simple plug gently pressed in, possibly simply held in the hand. The big lump of glass would remain hot long enough for the plug to be squeezed in with little pressure, then withdrawn and perhaps a little free forming done afterwards.
When I was a student, we (unofficially) made ash trays this way. The plug had four rods sticking out of the sides to form cigarette grooves. No press of any sort needed. Final result was, let us say, primitive art!!