iirc, the games you listed as working require only 512K RAM (not sure about Another World though). I'd try more of 1Mb RAM games.
The 'usual procedure' is to re-seat all chips (or at least press down until you hear crack) and maybe replace capacitors, test voltages too.
There was also an "Advanced Amiga Analyzer", some of its tests can be used without extra hardware, perhaps it can help.