My Japanese knotweed laughs at RoundUp. Use Ground Clear, multiple times, but most importantly in the Spring on new growth. I know you have plants you want to save but I've dug down over 12" and that isn't even close to deep enough to get all those fragile roots. If it has truly invaded your garden you may have to sacrifice that part for a year to keep it from spreading.
Also, understand you will NEVER be rid of it completely until the golf course gets rid of it. Let them know that they have an invasive weed & that they need to do something about it!
