Volunteer Plant (tree?) in Brevard County, Florida

I cannot identify this plant. I have searched databases but am not able to make an identification other than "maybe one of the 80 types of magnolia" ... I asked at two local nurseries and people suggested I simply remove it. I have asked local master gardeners who suggested I check with the extension office. I took photos and leaf to my county extension office with no success. I have sent emails to the UF botanical people but not received replies. I posted some photos on an equestrian message board and one respondent suggested I ask you-all for help.

So, please help, if you can! If it is suitably located, I am happy to care for the plant/tree. The butterfly garden I am trying to develop in the south-facing yard could use some shade.

The plant volunteered early spring 2015 near Helconia I had purchased at a local box store. It is located in mostly sandy soil at 28.4769° N, 80.7886° W (2 miles west of the Indian River).

Leaves are from 6 to 8 inches. The back of the leaves don't appear to be fuzzy at all; in fact, a bit leathery.

Young tree in August:

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Showing leaf on branch pattern and possible flower (August):

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Leaf and possible flower (August):

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Close-up of leaf bottom (November):

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Tree in December:

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Trunk/bark (December):

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Branches (December):

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Thank you in advance for help and advice!

 

Ficus of some sort.

 

I was thinking that too, and depending what sort, you might want to remove it, unless you want the shade to encompass your house and whole yard. The leaves looks similar to Ficus aurea, Strangler Fig, a tree native to Florida. I found a bit about it on this page:
Trees & Shrubs of Florida - Gallery 2

 

Thanks for your suggestions ... there are a lot of types of ficus to review. I did find a few photos online that showed the Strangler Fig as a stand-alone tree like mine, and the nearby text suggested that my front yard is not a good location. Ugh. Wish I hadn't waited until it was bigger than 3 feet to get serious about looking.

Thank you both so much.