Rick I won't yell at you because you don't hate Roundup. I myself like it for certain jobs. Certainly I physically remove unwanted plants when I can, and sometimes that is the ONLY way.
The previous owners had a trumpet vine on the lamp post. Roundup would kill it back but new shoots would just keep coming up. I had to dig up the area 3 times to remove roots. We'll see in the spring if I got it all.
Also, the previous owners had a whole bed of Chameleon plant. The only solution for that was to literally dig out the whole bed and sift the soil to remove all the roots! A hideous task that took WEEKS. And I am sure I will still find some small growth in the spring. But if I dig it up as soon as I see it I think I can eventually be permanently rid of it......maybe.....