At $7K per core for such a license and the number of cores you have, you should spend a relatively tiny bit more and get yourself up to 512GB of RAM.
According to what you say, your 1.6 TB Clustered Index is partitioned by 10 and so your partitions should be about 106GB so, even before getting more RAM, rebuilding one partition at a time should do it, especially since the rebuild should be doing Minimal Logging because you're in the Simple Recovery model. The rebuild should also be able to "go parallel" because you have the "Expensive Edition". That is, unless you set the system max dop to 1.
I'm not sure why TempDB should have blown out so much unless you're using the SORT_IN_TEMPDB option.