A better option to the discone is the bicone.? Sure, it's larger, but behaves a bit more like the LP over frequency, but without the directionality.? For his purpose, the discone may serve as the best choice.? I can't imagine what the Schwartzbeck costs.? It's a professional antenna widely used in EMC measurements for radiated emissions.?
If he really wants bandwidth, build a disc dipole.? I recently built an ugly version.? It measured well at or (mostly) under 2:1 from 135 MHz through 3 GHz and the pattern is dipolish.? Off hand I am not aware of anyone marketing such an antenna.? Someone should!