Hi ActualGuyFieri:
I've eaten at your restaurant in downtown Louisville. Nice, and great aroma.
As to this tree: I think you don't have to worry about its identity. Northern Catalpa (Catalpa speciosa) can have entire or 1 to 2 lobed leaves. Everything you've described about it (but not given many images of it) tells me that you have a parent Northern Catalpa.
This should be an object lesson to you and all that wish to propagate plants: DOCUMENT DOCUMENT DOCUMENT. Take prodigious pictures of plants you like, collect from, and grow. Then - when you inevitably have questions like this - you can produce the imagery that can help answer the questions. That, or fly us in to your place in Jersey, and we can sort it out directly and then go get some good eats.
I used to travel to south Jersey (Millville) a couple times a year to the Holly Society of America board meetings. Loved going there, seeing great plants, and eating well.
