Measure phase difference with less than a full wave?
Use a chirp!

Setup a low power transmitter, CW in say the 24GHz band (smaller antennas) arrange for it to sweep in a linear ramp upwards in frequency by maybe 100MHz or so over a few tens of ms. 
In the middle of said sweep you use a mixer with the IF fed from the transmitters output to mix with the reflected RF. At the mixer output you get an audio tone frequency proportional to range to target, process as appropriate. If you have much vertical movement you may want to average the result from an upward and downward sweep to reduce the impact of the Doppler shift. 

A completely alternative approach:
Why not take a leaf from Bomber Commands book, specifically the dambusters mission, where they measured altitude by mounting two searchlights on the airframe spaced some distance apart and mounted at different angles, looking at where the two spots of light fell gave them a way to judge altitude. 
The modern approach is probably a quadrant photodiode with a collimator and a laser diode mounted on a servo, pulse the laser and use sync demod to detect the return then use the quadrant photodiode to adjust the servo to centre the reflected spot in the diodes field of view, you now know the angles, so altitude is just a case of trig.