40+ years in landscaping here... and licensed to kill... weeds...
Do not cover stone with straw, that would make a mess.
Straw/mulch does not go over weed barrier, stone does.
Buy a sprayer. Spend a couple of bucks and get the battery operated one. Mix both a Roundup product (glyphosate - which is Ranger or any number of products) with Weed-B-Gone (or any other broadleaf weed killer). Start at a rate of 2 oz per gallon of each and go up until you get the effect you want.
The Weed-B-Gone products act like a strong fertilizer and accelerates growth, burning the weed. That acceleration helps the Roundup work too.
Spray early morning when it is cool. Plants do not take up weed killer unless they are growing. Add a little Dawn dish soap if you want. That helps spread and stick the product.
Once a month should be all you need.
If you are hiring a company, they are likely not coming in the morning. But if you are unable to spray yourself, at least leave your sprayer out for them to use. They have to mix according to the label, and that may not be strong enough. And surely, they will not mix the two products.
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It's all downhill from here!
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