If you don't mind home-made, quick fixes I've got two ideas for you(both worked flawlessly over months of NY messengering, 'back-in-the-day' ):
Take an old mtb inner tube & cut out a square of it, approx. 2.5 x 2.5 cm(you can even use the section from around the base of the valve, slightly thickened and pre-shaped for a circular projection!
Make a neat little "x" cut w/an exacto or razor blade or if your handy carefully cut out a circle smaller than the presta valve diam. Slide this over the new presta tube before mounting and it acts like a grommet
in the schrader rim hole. Cushioning and centering.
Head over to your nearest well stocked hardware store(the one w/the little drawers & shelves of widgets & fasteners) and ask for actual small rubber grommets or bushings that will perform the same job.
Since you mentioned, in no uncertain terms, this was your "beater" I don't think this will clash with any fashion/elite-ist, ego-pros you might ride with.