accuracy and automatic watches is a matter of money and / or luck and i would say in a price range that you are after it is rather luck than money, no matter if Tritium or not.
For getting only almost the same accuracy of your G-Shock with an automatic watch by price you would have to spend from 3.000 Dollars upwards and also a COSC certificate does only mean that the movement worked at a sufferable accuracy (compared to the vast mass of Quartz watches) at the date of testing.
Beside the above mentioned, the accuracy of automatic watches depends on many factors, starting with the way you lay your watch onto your nightstand...
Automatic watches do also need regular maintenance, what means that you will roughly have to plan spending approx. 10% +/- of the retail price for this all few years.
There are "cheap" automatic watches such as low range Seikos, Citizens, Orients, Maurice Lacroix... that can show pretty good accuracy too but as mentioned above, this is rather though their movement than because.
So in my opinion you should not consider buying an automatic, you will very likely only be disappointed.