But control for drift so it does not kill the "nice" plants.

vinegar kills plants...honestly.
You may have to re-spray every 3rd day till the thing dies, but you should see results by day 3.
Of course, if it rains or snows, re-apply.

The roots however can grow almost a foot deep and spread. Still, I will try.

So a persistent spraying of the leaves will starve the roots.
tho new shoots will perhaps spring up and call for more spraying till you see them no more.
Whie vinegar is pretty cheap in a gallon size keg,
And you can cut the vinegar with water by as much as 50%.

I have been fighting it for over 20 years. It is easy to pull out though, but you have to keep after it. Like you, I don't want to use a week killer around my good plants. I start yanking it as soon as I see it. If you let it go, it takes over.

So I suppose I will have to do this again for 4-5 times in the year.

I would do it every freaking day...or every time you see it popping up anywhere. I find that pulling a week when it is small and there are few is much easier than designating one or more days to trying to pull everything that is there, some of which may have already bloomed and seeded.

Good luck---you will be doing this forever. I don't think there is a way to get rid of it, you can only manage it.

Before I had a yard of my own, I thought it was very pretty, a wild morning glory climbing everywhere. Now it is the bane of my gardening existence!

I have read that you can exhaust the roots by pulling it up the second you see it, though it will probably take years to eradicate it. I have been doing this now for two years. Not having much luck at all in the vegetable garden, but my flower bed seemed to have less at the end of last summer. Maybe I was just a bit more obsessive with the flowers than the vegetable beds since I made the flower bed from scratch and the veggie beds are well-established. Anyway, I've avoided the vinegar route because I don't want to damage my other plants, and also, I find the vinegar works about as well as hand-pulling.

Good luck and let us know how you progress with your eradication project!