Let us start by saying there are two things we don't like-the first is the use of non-native plants, such as Paulownia tomentosa, Princess Tree. The second thing we don't like is trying chemical fixes that endanger other plants, animals (including humans) and the environment. From Texasinvasives.org, in which the Lady Bird Johnson Wildflower is an active partner, read this information from the Texas Invasives Database. Mr. Smarty Plants never recommends plants that are neither native to North America nor to the areas in which they grow naturally. One of the main reasons for this is the possibility of invasiveness, taking over and pushing out natives that are adapted to the climate, moisture and soils of the area.
We do not pretend to be an expert nor to have any experience with the methods suggested but we will refer you to a couple of websites that seem to contain the information to which you are referring:
DCNR Invasive Exotic Plant Tutorial, Species management and control information on Paulonia tomentosa
From the University of Kentucky, Forest Health-Invasive Plant Hit List: Paulownia
We urge you to read all the information on these websites before making any kind of decision, and also to consult with a trained and licensed professional in the application of herbicides. We also frequently recommend that you start with the local Extension office, which may be able to steer you in the right direction on local laws and rules on herbicides. Your office is University of Maryland Extension Office for Carroll Co.
One last word: the best way to deal with an invasive plant is to never plant it!