I missed a couple of points in your original post, like your using the A3 already.

You can check the external things first, like Spaceworm suggested. I would also tighten down the backplate and change the fuel line from remote needle to the carb. Change your vent line from the muffler, even if it looks good. They can get hot and collapse after a minute or so of running.

The engine is easy to disassemble, and parts are cheap. Have you checked the crankshaft to see if it is still true? Inspect all around the crankcase with a magnifying glass and look for tiny cracks, especially around the mounting tab area.

Have you tried fuel from another jug after emptying your fuel tank?