To get an idea of how much force will be placed on the turnbuckles and the wall, see this thread.
I think you will find it quite challenging to remove and put up the cables after the cables have been strung and cut to length, even if there is no net strung from it, because the sideways force is so large. Picture yourself standing on a step ladder, with more than a hundred pounds pulling sideways. Probably the ladder will tip over.
Really long turnbuckles might work, but also consider putting in two eyebolts on one of the walls. One would be attached at the intended cable height, and the other below the first by several feet. Run the cable through a pulley attached to the top anchor, and attach the cable and turnbuckle to the lower anchor. Putting tension on the cable in order to remove or reattach the cable from/to the lower anchor is done with a straight down pull, and that's much easier to generate than a sideways pull. Probably body weight would be enough. Then you'll be able to remove/attach the pulley with very little tension in the cable, because you've temporarily added a yard or so to the horizontal length of the cable when it is disconnected from the lower anchor.