The difficulty with calculating by hand is there are some checksum bits. If your goal is to overclock the ram to maximize its performance, you probably have to do it again and again for servel times so that the ram reaches its best performance without failing the memtest (the higher the speed the more likely to fail the memtest). Without a tool or a script the checksum bits has to be calculated everytime by hand...I am calling for a tool to make this eaiser...
Possibly you don't need to invest extra money (but just some time) to use that tool. Thaiphoon Burner has a free version that it does not allow you to save the spd.bin but it has a hex editor that can show you the modified hex bits and the calculated checksum. It can be used as a reference. Then manually modify the spd.bin file and write it using some free tools (e.g., RWEveryting on Windows or eeprom/i2c-tool on Linux).