I did try to install it from the website. However Zorin would not let me install. Said I must use the version they provide, in the software library.

Strange. With new versions of Sweet Home 3D I don't install. I download the 64 bit .tgz file and extract it next to other versions I have. This can basically be anywhere you want. I have all versions on a separate partition for Sweet Home 3D on a data disk. Simple as that.
Since the home .eteks folders are already there this should work just fine. Start with the SweetHome3D-Java3D-1_5_2 script in the extracted directory.
This is on Debian. Ubuntu is based on Debian and Zorin is based on Ubuntu so this *should* work.
If you have the memory available you can try to increase the amount of memory Sweet Home 3D is allowed to use by changing the -Xmx parameter in the startup script, for example to -Xmx4g or -Xmx6g.