J Sheriff,
I know our members well enough to know they aren't trying to ignore your request or brush you off. There is a lot of experience here, but certainly not the answer to every question.
In answer to your direct question, I have not tried white vinegar on stainless burner tubes. I did have good success with it on light surface rust on flat 304 stainless exterior panels. Burner tubes are obviously very different with high heat burn in compounding the problems. I can see the possibility of the burner holes corroding beyond just solvent (vinegar or rust remover) ability to take care of. In that case, the suggestion to use a paper clip or appropriate small drill bit is not out of line.
I have used a rust remover called EVAPORUST (available on Amazo). It isn't cheap, and it does take time to work, but the good thing about it is that it does not rely on caustic chemical to break down rust. I don't know whether it would work for you or even if it is cost effective.
At some point, depending on the time and materials you have on hand, it might be worthwhile to just buy a new set. There are a number of after-market, low priced options. Here is an example - not saying they are the best but look at the price vs. your time:
https://www.amazon.com/exec/obidos/ASIN/B011S23ODI/tvwb-20
Now, if you happen to have the older Weber 304 (non-magnetic) stainless burners, I might be willing to put more time into a set of those. Still, if they are corroding anyway you do have to ask how much more time and effort?
Best wishes! We DO want to be as helpful as we can to fellow members.