You haven’t provided any info about your partition scheme for either drive, but I assume you’ve got your bootloader installed in an EFI partition in the newer drive. You will still have an EFI partition on the old drive created by the Ubuntu installer, so just be sure you know which bootloader you’re using.
Option 1 and 2 aren’t functionally any different. It’s not clear what issues you’re worried about, but if you’re nervous about breaking the Ubuntu installation, you might just want to wait until you can get the new drive.
You also don’t give any indication of how much data you have that you want to keep. If the 2tb drive is almost full, you have fewer options than if it is mostly empty or half full. You could resize your EXT4 partition and create a new partition, for example, allowing you to mount a fresh, clean filesystem to a subfolder in your home directory. Once the data migration is finished, you can format the old partitions and mount them somewhere else, or resize the newer partition over them. Be aware that your HDD will eventually fail mechanically, however. Maybe 5 years from now or next week, but they all fail someday.
It’s not clear to me what the goal of option 3 is, but it’s dependent on how you use your machine. If you want to install a lot of applications or games that you want to run fast, you don’t want to migrate a bunch of your data to your newer SSD. If you just want a temporary place to store the data you want to keep until you can format the old drive, I guess this is a fine approach, but creating a dedicated user for this is just adding unnecessary complexity, IMHO.