Rather than a dual channel 'oscope, could the two waveforms be applied to a differential amplifier such that when they are in phase the output of the differential amp would fall to zero.
If the waveforms are out of phase, the differential amp would produce a positive or negative output depending on the phase, leading or lagging. This could indicate capacitive or inductive reactance.
A simple output indicator could be a center zero meter or LED's.
The idea is reasonable but the problem is that the two signals will most likely be of different amplitudes so the difference will not necessarily be zero when subtracted. Typically, both the voltage and current amplitudes change while tuning around resonance which further complicates a subtraction. Since the equivalent circuit of the antenna system is a series RLC circuit, maximum current will occur at resonance so for tuning all that is needed is some means to indicate the relative current amplitude.
One thought I had about a phase sensitive circuit, but haven't pursued, is to couple the voltage and current waveforms into a 339 comparator set at zero crossing. The outputs would then be square waves of a fixed amplitude, each rising at the respective zero crossings. If these two signals are then sent to an exclusive or gate the XOR output would be zero when the phase difference is zero (at resonance) or just subtract the two square waves as you suggested by connecting the meter between the outputs.
There are other simple techniques that possibly could be used but the ones I know of are for power line frequencies or are frequency dependent. One such device is a "phase sequence indicator" which is used by electricians for three phase work. There is another called a "syncrometer" which is an electromechanical meter used when switching generators on line but both of these devices are for power line frequencies.
Neil