The first thing Id do is a test to verify that the converter + 1.5v alkaline cell is actually making contact in the Canonette. Id inspect the cameras terminals carefully to verify that they properly contact the body of the converter and the end of the 1.5v cell installed in the converter.
It might be possible for the combination to fail to make contact. You can measure the stack height of the combination with a micrometer or dial caliper by placing small pieces of paper over the ends of the stack (converter + 1.5v) to insulate the terminals. Then do the same with the 1.5v 625A replacement cell. They should have the same height. If the converter + 1.5v cell is shorter, then the stack might not complete the circuit.
Place a cell in the converter and measure the output at the converter terminals. Test both the voltage and amperage. Its possible that the voltage-reducing circuit of the converter drops the amperage too much for the Canonette to operate properly.
There is some useful information here that might help.
http://www.butkus.org/chinon/batt-adapt-us.pdf
The instructions that came with my CIRS MR-9 converters recommend the 1.55V silver oxide cells rather than the 1.5v alkaline cells. I dont know if matters, but Ive used the silver oxide cells as recommended and had good results with a Nikon FTN finder. With the converters it gives similar readings to other meters of know accuracy.