I found something that works. I have these lines in the vmx file now:
vmmouse.present = "FALSE"
mouse.vusb.enable = "FALSE"
I found that mouse.vusb option in a VMWare article here. I have since installed VMWare Tools both with and without its USB and PS/2 mouse drivers. It doesn't seem to make any difference, the mouse pointer now moves fine programmatically in the guest. Although when I finalize things I'll probably just install without those drivers to be safe.
Also now when I click in that guest I'm automatically at the cursor position in the guest.
Also I have re-enabled 'Ungrab when cursor leaves window' and 'Grab when cursor enters window'. We prefer those preferences for the other VMs and with the two lines in that guest it appears that for that guest only it does not grab when the cursor enters the vm guest window (I have to click in the window) and it does not ungrab most of the time... but not all the time. I can fling the mouse out occasionally.
One bad thing about this is that in that guest VM now I can't use the back or forward buttons on my mouse. I used to be able to use them to control the browser in the guest but now I can't. The left and right mouse buttons work though.
related article here:
Bug: WinAPI Mouse_Event() and SetCursorPos() broken in VM's?