Another thing worth trying is to mess around with the partition structure of your 2TB disk. Go to Computer Management > Disk Management and on your C: partition, right-click and select 'Shrink Volume.' Let it figure out how far down it can shrink it. Now in the lower panel you'll have the C: partition which is smaller (let's say 1.2TB) and some unallocated space. In the unallocated space, create a new partition and mount it as D:. Now move files from C: to D: that you want to keep but aren't part of the OS. Also be sure to do a Disk Cleanup on C: and possibly even shrink the recovery space that's reserved (Right-click My Computer > Properties > System Protection; for C: click Configure; you could try turning it off and deleting the current restore points for maximum effect though you'll no longer be able to restore to a previous time).
Once you've managed to get a lot of data off C: and onto D:, you'll be able to shrink C: again. Then you can expand D:. The goal would be to get C: smaller than your new SSD and D: to be at least 1.75TB. You likely have a good deal of media or Steam games, both of which are easy to transfer to D:. For Steam games, you'll want to Backup the game onto D: and then uninstall it. For media, you just copy it. You should *NOT* touch anything in C:\Windows, C:\Program Files, or C:\Program Files (x86). You *may* need to uninstall some large programs to get under that 250GB capacity limit. You can also download the installers and save them on D: as necessary while you're doing this to save some time.
If you've managed to get C: under 250GB, congrats. Now you want to clone some *partitions* rather than drives. Select the smallest two partitions on your HDD to clone to the SSD and you should be OK. The tricky part is going to be the bootloader. Typically if the MBR (master boot record) isn't cloned properly then the SSD won't actually boot. You can typically solve this by using the Windows installation media and entering Recovery mode rather than install mode. For this I would suggest you unplug your HDD so you can't possibly have it detect the HDD's Windows install.
If you get it to boot with the HDD unplugged, congrats this worked. Now you want to plug your HDD back in, enter the BIOS and establish the boot priority so that the SSD is chosen first. Boot back into Windows, and go to Computer Management > Disk Management. Confirm that the C: partition is on the 250GB SSD and that you have, in all likelihood, D: and E: on the HDD. D: is your old Windows installation, it's an exact copy of the current C: on the SSD. You can delete that partition. You can also delete the small unmounted 100MB partition on the HDD. Now you can expand that 1.75TB partition to take up the whole drive, 2TB, and change the drive letter to D:. You should find everything you put on the D: partition before the SSD is there now.