Field In Sight
As far as physics and especially dynamics are in question, you are right, all of you, including sandwiches and the spamcan itself were experiencing free fall and the load factor on the airplane was more or less 0 g. And if you went progressively (and I stress that) from pulling to pushing, there is no reason why the load factor would go significantly under 0 g.
If you could have plotted your trajectory, it would have been parabolic.
Nevertheless, as the airplane was in free fall, it was accelerating
at rougly one g, i.e, increasing its vertical velocity by 10 ms/s (20 kts) every second.
This means that your TAS was building up, albeit slightly slower as long as the dive was not too steep.
The main issue in this case would probably be the exit manoeuvre (sp?) hopefully early enough, gentle, and before the ASI was in the yellow arc, not even daring to think of the red line.