The continuous, splice-able rubber belting sounds like a good solution
but it might not be available.  McMaster-Carr does not have it, as far
as I can tell, and they have most stuff like this.

I bought urethane in a variety of types, both round and Vee section.
It works very well but there are a number of factors that need to be
considered.  I did not use it for a long span so I did not have the
vibration problem.  I'm sure this can be controlled by adjusting belt
tension and or using an idler.  Below are the problems I did have and
the solutions:

1. The color is either bright orange or clear.  Urethane is quite
porous and can be dyed with fabric dye.

2. Squeaking on pulleys.  The manufacturer recommended a very light
coating of mineral oil.  This does not cause slipping and eliminates
squeaking.

3. Stretch over time.  Urethane belts will stretch quite a lot
initially and then will maintain their length.  The manufacturer
provides suggestions for getting the initial tension correct.  If you
make your own belt, you can start with it rather loose and tighten it
as necessary until it is right.  If you buy it made to order and there
is no way to adjust the position of the motor, you may have to try a
few times until you get it right.  Most of the old pulleys had Vee
angles different from modern ones and the belts were also a different
width.  This makes it a little difficult to determine the required belt
length without actually fitting a belt.

If you can deal with the above issues, urethane belts are very good and
quiet.

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