I didn't really give the drum a full workout with the original heads and snare wires. I played a little bit but I do think the snares fully disengaged. I will have to look at the original snare wires to see if they are stiffer than the Gibraltar set. Also, the plastic straps on the original were very thin. The thinness might have added to the pliability to allow the snares to drop a little bit lower.
The Gibraltar snare wires are on the cheap side. They work in a pinch, but over they years, I've not had good luck with them long term. You're probably best to get a set of Puresound Vintage wires and use proper snare cord, rather than the plastic straps, or tape as some call it. I had a '63 Krupa Sound King for a little while. It had the zoomatic and the "extended" butt. Someone had cheap wires on it when I got it, sounded just meh to my ears. I got a set of the Puresound vintage wires and it sounded great after that. Didn't have an issue with snare buzz or "not turning off", as you state, after that. I was using a Remo coated Ambassador for the batter head and a 3-mil Remo hazy snare side.
Sometimes it takes a few attempts to get one of these snares to sound at its best.