Glad it is healthy and growing. Nice flowers.
Probably 'Jackson's Tuscan Sun' as Jackson-Perkins was one of the largest commercial rose producers in the USA.
One option would be to try to air layer right at or just a touch below the widest point of the knuckle. That would get rid of the long neck between the nebari of the understock and the 'Tuscan Sun' portion of the rose. It would also leave you with the understock as a separate rose for training. Both knots of wood look over 2 inches in diameter, and real ''trunks'' in roses are rare, so it would be worth preserving both as separate trees.
You can also take late summer cuttings of 'Tuscan Sun' portions, (semi-hardwood cuttings). They will root over the winter. I have gotten roots without use of any rooting hormones, but only about a 33% take rate. The cuttings will be on their own roots, and since you are in a Florida climate, they will be just as vigorous or even more so than the grafted roses.
Grafted roses are quicker than from cuttings, so this is the commercial propagation method by choice, but most roses on their own roots are just as vigorous as any of the grafted roses, once they size up. Occasionally grafting is done to increase winter hardiness, but except for those of us in zone 5 and colder, almost all roses are winter hardy in zone 6 and warmer.