...4 feet in 4 months... Automatically disqualified from keeping for me.

Excellent point! Yet papayas grow even faster...I also bought a miniature pomegranate that came with a few stray papaya seedlings.

I was hoping beyond hope that the mystery tree was another fruit tree of some sort!

It may be a Bischofia tree. A softwood nuisance IMHO.

Looks like a spindly ficus to me....

I agree with Tom - looks like a Ficus to me.

Gumbo Limbo?

Does the trunk get fatter at the soil level with flaky reddish bark?

It might be a Java Plumb, Syzygium cumini. Catagory I invasive exotic. Large messy dirty tree, trust me you do not want this one!

It looks like a bay tree. I have them all over my property and they grow fast.

My guess is carrotwood - a true pest & very fast grower....

Many, many thanks for all the suggestions! I will have time to research this today or tomorrow to narrow down the results...and it is leaning very heavily to this thing being yanked OUT!!!

OK, looking twice (didn't see the closeup last time), I take back the carrotwood call - looks more like a banyan or similar.

Maybe a camphor tree. Crush a leaf and smell it.