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#11
Just in case you are still wondering, I can confirm that the H7 will not fit comfortably in a 180mm wide case. I have an H7 in a 200mm wide case and there is around 1.5cm of clearance after fitting an Intel CPU. In addition, it is difficult to fit large Coolers when there is so little space to work in.
Looking at the specs other than the case dimensions here,
ASUS TA-8G1 w/o PSU computer cases specifications
personally I would be looking at a new case to go with new components. Anything new is likely to be starved for air with only 4 x 80 MM fans for airflow, that or to get enough air in the case you will likely go deaf from the noise of fans that small.