This isn't an area of expertise for me, but here goes. I would like to say that, in my opinon, this isn't a Wine vs Crossover problem.
First, I would recommand 664 for security considerations. You don't need to execute anything on you usb device, you need read/write, and 664 will give you that much without execution. Not that I can think any situation where this is dangerous off the top of my head, but why not go for better practice.
Secondly, every reboot will change the permissions back, so you have to do the same commands over and over. You can solve the problem with a udev rules that should set permissions for you. Something like /lib/udev/rules.d/53-serial_usb.rules, with the rule as:
ATTRS{idVendor}=="03f0", ATTRS{idProduct}=="2504", MODE="0664"
The two attributes (ATTRS) should be made available to you with lsusb command. I'm not perfect, so if this doesn't work, google is your friend.
Lastly, from boot to boot and port to port, your device might not always be on ttyUSB0, it might move. So at each reboot, or just moving the device to another port, it changes where the device will be on the system. I imagine a udev rules could help in that are as well, but you might also need a systemd service file. A good article can be found here.
You're delving in a somewhat complicated subject, but if you resolve this, you will have learned a bunch of stuff many wouldn't even know is there.