I am way too lazy to download it and test it right now so assuming it is an old school leave some fingerprint on the system type deal and not detect IP, email and communicate with the mothership to send system fingerprint then a few options. I also assume winding the date back a few days won't have it spring back to life -- it used to be a thing back when.
1) Find if there is some other means of setting the printer up. Stock installs for many distros (even ones like Mint) are not that great so see what else is out there. I don't know offhand what exists to make Windows drivers into Linux compatible ones like we saw for wireless cards some years ago but if that is an option then great. It might also be a matter of tickling the Linux stock CUPs driver in a text editor to allow for the higher DPI if you think you want that (
https://en.opensuse.org/SDB:Print_Settings_with_CUPS covers something like what might be happening here). That said looking around it seems canon and canon drivers are not the best and quite complicated so maybe 600 is your limit.
2) Depending upon what you have to print then you can run a liveCD in a virtual machine, install the trial on that, copy the file across (or stick it on a network share, http, ftp... just make it available to the VM)
3) Again do the VM thing but with your particular distro (down to version if you still have the install CD or can get it) do an install of the OS. Do a backup. Install the program. Compare backup state (everything on Linux is a file remember) to new state (or possibly it uninstalled, and maybe you winding the clock forward to make it think the trial is over). This list of changes is at least one possibility (some programs have many locations that they might leave a fingerprint in)
3a) is install windows in a VM and just print it from that.
Do you really need more than 600dpi though? That printer tops out at a4 and unless you are printing on super high end coated printer paper... 300dpi is probably overkill really.