About this detail of the Tiger
An interesting feature of the turret on this special vehicle is that photographs ([3] page 371-376) clearly show it has an escape hatch. These hatches were introduced to the Tiger 1 in December 1942 ([1] page 83), after cancellation of Tiger (P). It's possible that they appeared in Tiger (P) at an earlier date, or that there simply isn't a neat cutoff date for the features of these turrets; after all, it took months to assemble each Tiger (P).
The above diagram shows the differences between the turrets from the Tiger (P), the first production Tiger 1, and the vehicle obtained by S.Pz.Jg.Abt. 653.
It's difficult to tell from the photos if the hatch is the early type (bevelled sides) or late type (flat disk). I built CAD models of a turret and hatch, reproducing the perspectives seen in the photographs, and compared them. I conclude that this is an early hatch.
[1] DW to Tiger 1