Has the wheel been laced incorrectly? EG is the valve located between 2 spokes that angle towards each other, limiting the amount of room for the pump head? Valves should be between spokes that run approx. parallel to each other for that reason.
Thanks for your suggestion, jur. I checked and the spokes are laced correctly.
I went down to R.E.I. this morning and purchased a Topeak JoeBlow Sport ($36) which is the only floor pump I've seen that has a head with a thumb lever that goes side-to-side rather than up and down. Hopefully, this should solve the problem, as there is no need to angle the valve to inflate tire.