Yeah, those linear pulls are something else and probably the latest generation of
brake design. My first ten speed had those cheap side pulls where the cable came down to one side of the brake mechanism. Later I got a better bike with the center pulls where the cable came down over the top and lifted up on the cable which ran from side to side. My first mountain bike had the "cantilevered" brakes where the levers pivoted off mounts welded on the fork tubes.
Perhaps you would want to go around bicycle shops and see if you could buy
a scrap bike or trade in to build up. If your worried about braking find one with the frame set up for the cantilevered brakes. You could probably get it for cheap.