After many miles, and lot of frustration, I gave up on the presta tubes. I prefer them... as I like the valve over the "Big S", but you can't get puncture resistant tubes with them. I tried slime, but no luck there. I tried even using "tire liners" (cut up former tubes, placed between the presta tube and tire), but no luck.
So... I gave in one day and bored out the holes and made the switch to "Big S". The one perk is that now my pump doesn't need to be switched to pump air into my trike and my two-wheeler!
But, now I have puncture resistance tubes, mountain bike kevlar tires, and no punctures in many, many miles.
One negative is that the Shraeder valves (at least for me) seem to have slow leaks. Not major... but it means pumping my tires up every week or so, something I never had to do with Presta's. This is true on my tubes, as well as my girlfriend's trike, so I can't imagine it's a "random bad tube", but instead a design issue with them. Not a big deal, though.
Also, finding a 20" presta tube while traveling is somewhat difficult. The shraeders, in a pinch, can be found in Wally.