In HDSDR changing of the LO freq causes a short audio dropout, because of this you can only change the receiving frequency for locking on a signal.
A further drawback is that the signal in the upper RF window is still drifting, but on demodulating this signal it is no negative effect, only an optical issue.
Someday a clever person will programm a SDR software that is capable of locking on a signal (in the bandwith of a RTL-SDR) and on a second (following) demodulator you can listen to SSB. That would be the nicest and easiest solution
vy73 DB8TF