Jake -
They did indeed remove the solid bulwarks at the waist (and lowered the high bulwarks along the spar deck)...
It was determined that the 1927 restoration based the solid version on plans and photos from the 1850's. It was mistakenly thought that it would stiffen the longitudinal strength of the ship to counter the buoyant forces that induce hogging. In reality all it did was introduce about 40 tons of stress down to the keel.
It was never, unfortunately, correct for the War of 1812 glory years.
We do, however, see that in 1812 the waist did have canvas cloth stretched across the front of the railing and painted black:
This is a close up of a contemporary paining commissioned by Commodore Isaac Hull himself and supervised by his purser Thomas Chew. The photo isn't quite sharp enough to show the detail of the fabric wrinkles of the stretched canvas that you can see represented on the actual painting (collection of the Peabody Essex Museum in Salem MA). Note the yellow stripe - that is a whole other topic...!
Santa - it would be very interesting to see someone build a Connie as she appeared during her great escape from Broke's squadron to start the war. The account from Moses Smith, who was on board that day, suggests that the number one 24 pdr gun was hoisted up from the bow of the gun deck and positioned at the stern to join the 18 pdr chase gun pointing out the holes hastily whacked into the taffrail. The stern gallery windows were also apparently smashed out to allow for a few of the 24 pdrs to fire astern. I don't think there is any other evidence to support the two long guns up on the bow during that escape.