Yes. (Those muscles/tendons in your calf would be your peroneals). But it also sounds like you have some some functional asymmetry going on. You might be dropping the hip on the other side, which causes you to reach farther with the injured side. Since you are maxed out on that cleat, you may want to try lowering your saddle a touch or moving it forward to alleviate the reach problem, and think more about whether you are sitting squarely on the saddle. I've had a similar problem, though not nearly as extreme in terms of cleat position, but the problem starts with my hips being functionally asymmetric. Eventually, I developed peroneal tendonitis. I was treating that tendonitis with PT, but nothing was helping for long. Then we discovered that my right SI joint was out (one day when I complained of an ache down my IT band and hip/pelvic pain). We started addressing that problem, and the calf has stayed healthy.

Another reason I suggest moving the saddle a bit is because you are straining yourself even more under load on hills. That suggests to me that maybe you are trying to drop your heel more than you can, and you wind up hyperextending that knee a bit, which causes the posterior knee pain. You of course don't want to aggravate the top of the other knee by going too low or too far forward, but you might be able to find a position that is a happy medium.

Also, go to cyclingnews.com's fitness Q&A page and look up the responses relating to functional asymmetry and cleat position. You may want to try moving the nose of your saddle a little towards the good side, which will force you to sit over to your bad side more, shortening the reach there. The fit expert on that page can explain things a lot better than me.