Could you share the laptop model, surely there has to be a way to turn off the disk encryption and then dual boot/mess with the laptop normally?
The easiest way to achieve that is to use two USBs, one with the installer, and the other will be your new harddrive. Install to the USB drive and it will be a persistent bootable USB drive. Bootloader (grub/efibootmgr) setup may be fiddly, you may have to try a few times/variations on setting before you get it working.