Keep in mind that Roundup is a systemic herbicide- that means it is absorbed through the LEAF. Most people who claim Roundup doesn't work used it improperly. Anything you spray on the dirt is wasted. I have found that any concentration over 3 oz. per gallon does not give better control either.
Keep your mix at 2 1/2 to 3 oz. per gallon, and spray the LEAVES of the ivy. No need to drench it, just enough to hit all the leaf area. Try to spray on a calm day when you don't expect rain. Follow up in 2 weeks to get any that survived. I also use a little sticker in the sprayer, it helps keep the glyphosate on the leaf longer.
I seem to remember reading that Roundup is about as toxic to humans and animals as aspirin. I have no problem using it.