In a near future setting (technology has progressed more or less at the current pace) would it be possible to have a genetically modified tree that has both the density and textile strength of Schinopsis_brasiliensis (see also this answer in regard to it's exceptional qualities Creating wood actually as hard as granite) AND fast growing properties like Paulownia (one of the fastest growing hardwoods)?
Paulownia grown on plantations generally has widely spaced growth rings, meaning that it is soft and of little value; wood with close growth rings is harder and of higher value. Paulownia is extremely fast growing; up to 20 feet in one year when young. Some species of plantation Paulownia can be harvested for saw timber in as little as five years.
Would 'fast growing' necessarily be mutually exclusive with 'extremely dense and with high bending strength' for a tree? Generally fast growing hardwoods have large rings. This leads to lower density and tensile weakness. On the contrary trees (even of the same species) with thinner rings are denser, with higher tensile strength but grow more slowly, usually due to less favourable climatic conditions.
The purpose of the company engineering the tree is to have a naturally fast growing hardwood that can sustain construction. To be shaped while growing. Imagine treehouses, bridges, monuments. Living architecture in general but brought more to the extreme (the living tree structure) and to a bigger scale than the examples in the link.
Economic sustainability is not an issue.
The purpose is not to have wood as construction material like with this method: Wood made denser and stronger. The tree must be alive and growing while being shaped.
Merging of trees, even of different species is fine. Grafting is also appliable. But the main structure of the tree should be of the genetically modified species (of which the company holds the rights).