How is your technique when running with the minimal trainers? Is it possible you are staying up on your toes pretty much the whole time? You need to ensure the heel makes contact with the floor, (obviously after the forefoot) but if you are up on your toes the whole time you run that would be very hard on the calves.
Also what foorwear do you use for normal day to day wear? I switched to flat shoes pretty much 100% as I found it helped to keep my calves stretched. If you wear shoes with heels all day you wil be shortening the calves, then asking quite a lot of them to run with a much flatter shoe.
I only wear shoes because my crap feet are too soft to go without. I plan on wearing my minimal shoes until they fall of me mid run. The only reason they are there is to stop me making holes in the soles of my feet, and I see no reason they would need to be changed at some arbitrary point.
You sound a lot like me. I started on the 0 to 5km program a couple of years ago tonget fit and lose weight. Didn't really enjoy to start but kept with it (something to do with reaching 40 and thinking I really had to do something).
Two years on I'm no super athlete, but I really look forward to going out now and enjoy my runs.
Summer is a tough time for me though. I'm happy to run in snow, ice and rain but as soon as it gets above 20c outside I know I'm going to suffer. I have to run less, run slower, and drink loads when I get back. I know what it feels like to keep sweating half an hour after the nice cool shower.
All I can say really is, enjoy the autumn. Must be my favourite time of year to run now (although winter and spring are ok too). I'm not going to be a great runner so I don't really worry too much about slowing down a bit in the warmer weather.
Keep going, with any luck you will push on through the 'doing it because I have to' phase and actually start enjoying it. I did, and lost 10 kg in the process. Good luck.