An interesting thought. Evidently the designers of the TMP refit weren't overly concerned that the shuttlebay extended beneath the where the support pylons connect to the secondary hull. With that in mind then why couldn't the TOS shuttlebay do the same?
Recall the only detail of the shuttlebay's fore bulkhead are the drawings in TMoST and FJ's Constitution
blueprints and tech manual. That fore bulkhead is never actually shown onscreen in TOS. Yeah, we see it in TFF, but I would discount that since the TOS E
is a completely different ship.
Here's another old composite for the fun of it.