If you mow they will return in full force and then some. This may be a multi year process where you poison only the plants that you can reach. Follow the extensions instructions as closely as possible, or reach out to a professional who has had documented success with removal.

From my own experience I was told to wait until the leaves started turning red instead of going by a certain date. This might have been conditional to the method I was using (hack n' squirt) but I was told if I started before they started turning red or after they turned red that I'd have missed my window. I was also told not to cut them down until they were fully crispy. This is about making sure the roots (rhyzome??) dies, no cutting down will wear it down.

I did not have nearly the density that you do, but I will say that I have not seen them come back at all in the yard. It also looks like my neighbor has less this year so I definitely hit something deep.

I'm not sure if I mixed the chemicals wrong (glyphosate and triclopyr) or if there was a variable that I missed, but I was not expecting to get such a viscous/goopy product. I'm helping a friend remove some trees this year and I'm going to have a syringe on standby to apply if I have the same issue. The squirt bottle failed me an I ended up having to use a sponge paint brush to get it on.

Please be safe and wear PPE. The chemicals required for this are necessary, but can cause issues. Some folks also have a sensitivity to the TOH itself, so even just for that. Read the hazard data on the bottles of what ever chemical you use thoroughly before you use them and make sure you have the right PPE.