As I recall there are two fundamental groups of phono cartridges,
which are distinguished by the output voltage level produced -- called,
amazingly enough, low level and high level cartridges.

The two varieties of low level magnetic cartridge are either moving
coil or moving magnet.  Of these two, the moving magnet has outputs
that are on the level of 0.7 mv (if memory is correct), and the moving
coil has an even lower level.

The basic types of high level output cartridges are crystal and
ceramic.  Both rely upon the piezoelectric principal, whereby strain
applied to the material generates an output voltage.  These are
relatively high output, as I recall on the order of one volt or so.

I am relatively confident that the original 78 rpm cartridge was of the
high level output type.  The flip-over cartridge that you substituted
could be either crystal or ceramic, and they were pretty well standard-
ized and used in most inexpensive mid-to-late 50s-60s phonographs.
Their output was usually fed directly to the grid of something like
a 12AX7 dual triode, minimally unequalized (i.e., no proper RIAA
equalization curve) which generally led to very "thin" sound, and
no bass.

These crystal or ceramic cartridges had an inherent high source
impedance which very conveniently matched reasonably well to the grid
input impedance of a vacuum tube without any added amplification or
impedance matching transformer.

If you have an oscilloscope or, more rarely, an AC VTVM or equivalent,
you could measure the output level of the cartridge, that is for 78 rpm
records only, to get an idea of the required input level to the
amplifier.  Measure it "open circuit", with the audio leads from the
cartridge not connected to the amplifier as well as connected.

Similarly measure the flip-over cartridge's output.  If you find that
the output of the flip-over cartridge drops significantly when
connected to the amplifier, then there is some kind of impedance
mismatch that is dragging the signal level down.  (Don't overlook the
obvious:  Is the wiring from the cartridge to the amplifier okay?  Could
there be a short in it?)

If the output pretty much the same whether connected or not, and not
comparable to that of the 78-rpm-only cartridge, then you probably
need an audio step-up transformer or some intermediate gain stage of
amplification.  If it plays at all, but just not loudly enough, you
probably don't need a bundle of gain; 6 to 12 dB would probably be more
than enough.

Harvey Chao