I have not tried splicing a round leather belt with glue so I have no
idea if the bond would be strong enough.  The little hog rings work
surprisingly well but are a bit difficult to install correctly.  You
have to punch a hole in just the right location and crimp the ring
carefully without causing a lump.  If you use an awl to make a hole,
it will likely be off center as it follows the grain of the leather
and will also split the leather making the connection weaker.

So gluing is a potentially reasonable alternative but I doubt that a
simple butt joint would be very strong.  Also, most CA glue is brittle
so it might be good to use the type that contains rubber.  This is the
black stuff that you can get at hobby stores for gluing model tires on
rims.

A long lap splice would probably be better than a butt joint because
there would be a larger glued surface and because the glue would be
in shear instead of tension, which might be better.  This would require
making a fixture to cut the belts at a sharp angle.

This is the way flat leather belts were connected.  They were also
sewed after gluing.  I have even seen round belts that were sewed.
I do a fair amount of sewing and know that this would be a real
challenge without the right foot and or guide on the machine.

Another consideration is the fact that round leather belts will
stretch continuously over time as opposed to urethane which will
stretch initially but then very little after a while.  This means that
you will be resizing the belt fairly often.

Punching a new hole and re-stapling would be much easier than cutting
and gluing.  I think the old belting was probably made of better
leather than the new stuff and stretched less.

Best regards,
Spencer Chase
Garberville, California
http://www.spencerserolls.com/