At 780kc on the grid dip comes in at 710 on a radio.
In that case then you are needing less inductance in the circuit , so rotating the slug outwards from the center of the coils plexus, with a non metallic alignment tool, should raise that frequency, for the correction which you are needing.
Check the purity of the DC on the instrument as per the health of the 60 and 10 ufd filters.
As per the abberations on the wave form. . . . .thats no rock steady osc ckt. . . . .take a finger nail and firmly tap on the case the of the unit and its result on the scopes response !
73's de Edd