It's worthwhile to check if one of the two outputs of a monaural goove is,
for a given side consistently inferior or superior.  I just did another
early 78.3 (rounded off)  lateral cut lacquer (1934) for Niel Shell (Nat
Shilkret was one of his Grandfathers).  The two sides were, thankfully not
gouged by prior playings with steel needles.   But it had been played
multiple times on those heavily tracking early systems.  One of the outputs
was dramatically less noisy than the other.

For vertical cut grooves, a method that occasionally (but not consistently)
is beneficial is to also digitize both outputs.  Keeping the eq. flat, then
apply your best available de-clicker to the two channel digital file.  THEN
sum them (with one channel 180 out).  When summing, interactively set the
two levels for a maximum lateral noise null. Whether done with early stage
declicking or not, always check audibly and or visually.  You'll often find
that the two levels are NOT @ unity.  Assuming that your preamp & cartridge
combo is properly set up, then when the level 'discrepancy' occurs, that
indicates
that the cutter was not functioning on a precisely vertical plane.  For
lateral grooves, with the critical difference being that the two outputs
are nominally in phase,  the comparable nulling is done to suppress the
vertical component.

For grooves that are intentionally neither vertical nor lateral (i.e. Arto
78s...with their audacious knock off of Victor's "batwing' label), it's
anything goes for selecting & possibly mixing outputs for the best possible
results.

AFTER the nulling is performed and two channels mixed together,  then
apply  eq. et. al.

Best,
Art (Shiffy) Shifrin