never had a Carlton but the mechanism is likely similar to most.
Parallel snare drums all suffer from various forms of misalignment possibilities. If you look at drum catalogues, almost every company lists one or more parallel drums as their flagship drum but if you pick one up off the shelf as a used drum , almost never does it sound great. Most drummers , much prefer a simple drop strainer and few companies still persist in making parallel models.
The problem is to get the adjustment right and few drummers are willing to put the time in to get a parallel drum working to perfection but clearly the companies that made them believed in them above all else.
It sounds like you have three problems 1) warped wires 2) the distance between the hangers is too close 3) one side is lifting higher than the other. This pretty much runs the gamut of possibilities for major problems, with a tight mechanism being the other big one.
I wouldn't put the blame on the wires until you have mounted a good set of wires, so in lieu of finding a set of good ones, I always opt to make the existing ones as good as possible. Sometimes this comes down to using the ends only and soldering in a new set of straight wires but if they aren't horrible, take the wires off and put them on a bench . Sometimes working each wire with two small sets of pliers can get them into shape and sometimes( usually) if there is stretch involved, after I straighten the wires, I clamp one end, clamp the wires nice and even , then desolder the other end and resolder it. This should give you a set with even wires and the stretched ones will work about as well as the ones that weren't.
After mounting, maladjustment in the mechanism can be addressed. There are two issues. The width adjustment and the height adjustment. From your description of the condition in relaxed mode, it sounds like there is too little lateral tension on the wires, causing them to curve upwards and contact the head. There is usually a tensioner on both hangers but your pictures show only one and it looks like nothing is missing, so I guess that is the tensioner. Lateral tension is set for the requirement when engaged and should not change when the wires are dropped. If it does, then the hangers are not dropping in parallel.Check the mounting screws of the hanger mechanism and see if there is any looseness, warped wood or missing shims. Those two end mechanisms, sometimes have built in adjustments for lift height or can be adjusted by sliding them up or down on the screws before tightening. The two snare hangers must rise to the correct height for perfect parallel head contact and drop in perfect parallel unison, otherwise the snare wires will not do your bidding. Sometimes, shimming the bottom or top mounting screws will get a hanger to move in parallel.
