At first glance it looks like a [url=https://en.wikipedia.org/wiki/Banana]banana plant[/url]. Then the next thing to come to mind is a [url=https://en.wikipedia.org/wiki/Loquat]loquat[/url]. Finally, it brings to mind a [url=https://aggie-horticulture.tamu.edu/interiorscape/Brassaia_actinophylla.html]schefflera[/url], although it only has 1 leaf per 'unit'.
Could be a 'Banana Shrub' (Michelia figo), but the unfurling leaf (you're right, Lorax) leads me to believe it's more likely of the Araceae family, possibly the Arisaema genus.
Because Ficus elastica is only hardy in zones 10 and 11. F. elastica could possibly survive in a microclimate of 8 or 9. I suppose there could be a cold hardy ecotype out there that I don't know about. That plant photographed is growing in Georgia.
I don't know if you ever figured out what your mystery tree is however I took this picture of a Southern Magnolia that I have in my yard and it does look very similar.
Watch your tree closely when it shoots out new leaves. It's really an interesting process to watch because they bloom, grow new leaves, and drop old leaves all at the same time. The plant in the photograph above has a leaf unfurling with no bloom present. It just doesn't work this way with magnolias.