Grumman AA5 Pilot reported they climbed and turned to avoid an opposite direction VFR aircraft which misunderstood ATC instructions and climbed to their altitude.

Narrative

I was in cruise flight with the autopilot engaged in heading and alt hold mode on vectors due to the rarely active restricted area being hot. The airway clips a portion of that area; so ZZZ vectors IFR aircraft around the area when it is hot. I was prepared for this; as it was on ATIS when I departed and ZZZ did not vector an unreasonable distance from the route and shoreline. The problem is that; when this area is hot; it puts most piston singles in a relatively narrow area where pilots are in comfortable gliding range and a reasonable distance outside the restricted area. The Controller working the ZZZ/ZZZ1 area frequency; which I've noticed tends to be the busiest in the area; was busy; but not overly. As they were about to hand me off to the other area Controller; they gave me 2 traffic calls at 12 O'Clock. Two VFR Cessnas at 5500 ft; 500 ft. below; that were on frequency; at something like 2 miles and 5 miles away. I read back and started looking for them. They gave the same call to those aircraft; stating that a Grumman was at 6000 ft. at 12 O'Clock and my distance. The first Cessna read back 'six thousand;' which I clearly heard. Before I could say something; the second Cessna was also given the traffic call and stated where they were. The Controller then handed me off; having not corrected the Cessna that said 'six thousand.' As I was reading back the hand off; I noted that they should check the read back with the first Cessna as they said 'six thousand.' I then switched to the next frequency. As I was doing that; I saw the first Cessna clearly in a climb directly toward me. I immediately disengaged the autopilot and put the airplane in a climbing turn approximately 800 FPM and close to 40 degrees to the right. The Cessna seemed to then lower their nose and pass off my left. I told the area Controller that I was maneuvering to avoid and that there had been a problematic read back. They understood and stated to 'do what you need' and then when able to fly a heading to intercept the victor airway. I may have climbed to an indicated altitude of approximately 6200 ft. before returning back to my assigned altitude and assuring the aircraft was properly trimmed and reengaging the autopilot. I did not have to enter the restricted area; nor depart my assigned altitude by more than 300 ft; though I would not have hesitated to do either if I had needed to. I assume the previous Controller called the Cessna after I made my comment; but don't know.I understand that the VFR aircraft have lower; workload permitting priority; but sometimes I think the Controllers just are not tuning into what they are reading back quite enough to avoid this kind of issue. They also seem to prioritize separating commercial and corporate IFR airplanes to lighter piston ones; even though we are the ones usually seeing these situations more often. ZZZ Controllers are the best I've dealt with; but these issues need to be discussed. Additionally; the military needs to really figure out whether it needs to keep the restricted area at all; as it causes a lot of confusion with unfamiliar pilots when it is usually cold and it causes issues with traffic when hot.