Consistant close cutting/mowing is about the only control outside chemicals and digging.

Dig out the roots. There is some evidence that appears to show that Johnson Grass, and Quack Grass, have the ability to detect when plant poisons are sprayed and the plants shut down to keep those poisons from reaching the roots. There is also some speculation that both of these have picked up the gene that makes some plants immune to various plant poisons.

As I stated in my original post,
Digging is NOT an option!

So I guess I will just continue with my current
plan of attack,
Mow, spray, mow, spray, mow, spray. . . . .
On and on and on,
Into infinity.

Sure was hoping there might
be some other options out there. . ..

Rusty

You could pen hogs in the area,they root up and eat the roots, Not sure what you are spraying with but every herbaside I know of states in instructions not to mow shortly before or after spraying.

"Digging is NOT an option!"
Unfortunately digging these plants out is the only really sure way to eliminate them.

"You could pen hogs in the area,they root up and eat the roots"

LOL! I feel quite sure my neighbors would have plenty to say about that,
and none of it would be very nice!

" Not sure what you are spraying with but every herbaside I know of states in instructions not to mow shortly before or after spraying."

I really do have sense enough to read instructions.
I didn't mean I do either one shortly after the other.
There is a definite time lapse
between the mowing and spraying.

" digging these plants out is the only really sure way to eliminate them"

I was afraid of that.
But you can't blame me for hoping someone just might
know of a better herbicide than Round-Up for this purpose.

I know it's going to take a lot of time,
But I'm hoping that persistence will pay off. . .. .. .

Thanks all, for responding!

Rusty