I am one of the developers of SerialTool and I noticed your post and we thank you for the appreciations on our software.
First of all I wanted to ask you first if you have resolved the issue.
Since this modem is not our product, we cannot provide direct support, but I can offer some suggestions.
The manufacturer of the module indicates the transmission speed from 300 to 115200 baud.
Typically, for these modules, you should connect to the serial port and send a series of repeated AT commands.
So, AT + [CR], then AT + [CR], and then again AT + [CR] until you receive an OK response.
At that point, you can send the remaining commands. If AT commands are properly implemented to any AT + [CR] you MUST get an OK as response and you cannot go any further until you'll get to this point.
Please let me know if you made it.