Should I use a base to offset the sour in overripe sourdough starter?
Just remove 1/2 to 3/4 of the starter and feed the remaining starter as usual.  The process of feeding should reduce the sour and normalize the ph level.  

You don't need a lot of starter to keep it going. Sometimes I'll just keep a tablespoon and feed it 2 oz. water and 2 oz. of flour (100% hydration).  If I know I won't tend to it for a while (e.g. 3 to 4 weeks), then I'll make the starter a bit stiffer by adding a bit more flour.

As far as what to do with the excess, if your not going to toss it...
I vote pancakes or English muffins.  These are usually served with something that'll mask or lessen the sour taste (butter,syrup,jam).

Where do you keep your starter between baking?