Mike
It's been so long since I took my stanchions off that I forgot what the base looks like but from your post I think I can tell you what I would do.
If there is a through hole now I would use that to make my set screw locations. First find the right sized S.S. set screw by finding one that the "drill size" for the tap is just slightly larger than the existing holes. All taps have a specific drill size that should be used with them. I would start by finding a source for S.S. set screws like theses guys... http://www.boltdepot.com/Set_screws.aspx?nv=l and then find the set screw that is a little larger than the existing hole.
To drill the base you can do it with a hand held drill just set your drill to turn very slowly and apply firm pressure. A squirt of oil once in a while will help. Heat is what destroys drill bits when you attempt to drill stainless. So turning the bit slow with firm pressure and oil lubricant will work much better than trying to drill to fast and burning up the bit.
Once the holes are drilled I would put the tap in a hand held holder and turn the tap in slowly by hand. You can feel when things are binding up and when you feel that stop and back the tap out again. Then shoot some oil in and start again. It's a slow process but can be done more easily if you don't rush it.
The advantage of going in the original holes in addition to not having to start the hole from scratch is that the set screw will turn part way into the stanchion through hole and lock it in place.
That's my take but your mileage may vary :-)
JERRY CARPENTER - C147
A man can succeed at almost anything for which he has unlimited enthusiam.