That battery is a bit small in my opinion. I'd say somewhere upwards of 675CCA is needed. Im in the process now of dealing with starting issues much like you describe. This is my story, maybe you can get some hints or ideas.
This my second mini starter that has gone out on me after the stock style did as well years ago. The last one was a powerful MSD mini( a really good, expensive, starter). It would start the car fine cold but after warmup and shutting off would not turn over fast enough to start the car. I sent it in for a rebuild. Was informed it was roasted inside. The tech said it looked like it had not had enough voltage to the starter. He said you need 11volts, cranking. He suggested putting a volt meter on the battery cable at he starter and check my voltage while cranking the starter. Sure enough I had 9.5 volts. He said not near enough for the starter to live. I'm in the process now of replacing my battery cables with new, larger wire.
A heat shield is definitely also a good idea.
It seems to me that you are in need of a new carburetor for your other issues. Definately do a compression test and a leak down test to make sure there aren't valve or piston/ring issues. I've torn down my motor before to find broken rings in two cylinders and the motor was actually still runing prett well. Good luck.
