My reference to the advantage of using presta valves is due to their acting as a check valve. They only open when the pressure outside the valve is greater then that within the valve (barring accidental bumping the valve's "lock nut" of course).

To slightly tangent from the focus on the pump, which I agree is the real issue, here's a little device I was exposed to decades ago and carry in my bike bag. I've had the need to use it more then a few times over those years. It was called a "Damsel in Distress Device". Please excuse the somewhat sexist reference but remember this comes from an entirely different era and what was acceptable terminology then has changed these days. As is easily seen in the photo it's a Schrader valved pump chuck still attached to a few inches of the pump hose. (This one is from a MDI pump, one of the all time good values of yester years). Hose clamped into the free hose end is a presta valve supplied from a bad tube and whose base has been ground down, smooth with the threader portion. The Shrader chuck goes onto the SV that some still ride with and your nice frame pump, set up for PV because that's what your bike has, will attach with no chance of loosing the chuck fittings in the grass at the side of the road (while you swap over to a SV fitting). I have told dozens of riders/customers and a few have made their own. A few of them have thanked me because they helped some SV rider who went out pumpless. Andy