It would be a tall order to explain how to do this here in this forum; I have a spreadsheet for these predictions which I had to build out of necessity many years ago - took me some months. It will be well worth your time - this effort will pay off well for future work when you dont have access to a process simulator or you need to get some quick answers.
If your discharge pressure remains the same, then polytropic head would be lower with higher suction pressure, assuming mol.wt of the gas remains the same. Work out the new polytropic head and find the new operating point on the compressor curve(s). Or find the new speed that gives you this head at the same flow.
Beware of the limitations of the GPSA manual procedure; this will be a good start in any case. The ASME procedure does not rely on Cp/Cv predictions, and is more accurate, especially for high compression ratios and high operating pressures or non ideal gases such as CO2.
Else, a process simulator would give you the new operating point if you could punch in the Q vs. H vs. speed data.