How much power does the monorail need?
The main factors are acceleration (f=m*a), aero drag, and friction.  Acceleration only lasts until the monorail is up to speed and that happens quickly.  The monorail goes too slowly for aero drag to be measurable.  This leaves us with friction as the main cause of power consumption.

First, if you don't know where you are then how can you know how to get to where you are going? Here is the data on where we are: The monorail takes 400 mA to run on a circle of beamway. The test was run with 2 freshly charged batteries, after a short time to cool down from charging. Yes, I am an engineer and yes, I like data! ;) On to the test results:

2 AA Eneloop 1900 mAH (runtime is calculated from current draw and battery capacity)

Stock motor
400 mA (runtime > 4 hours)
2.80 V (drop from 2.87 open circuit)
1.12 Watts (input, * 40% efficiency = 0.448 W output)
22.5 seconds around 44.5" loop (~140" circle)
6.2 inches per second

Stock, Cab Only
350 mA: so just pulling the rest of the train takes another 15-20% in power.

Stock, diaphraghms removed
400 mA: I thought these were contributing drag around the curve but it appears to be not much.

Stock motor, regeared* (drive wheel slipping)
500 mA
2.85 to 2.70
1.35 Watts
20.2 seconds
6.9 inches per second
a little better than 10% improvement even though the drive wheel was slipping much of the time

Stock motor, regeared* (drive wheel fixed)
500 mA ? (forgot to measure it)
17.7 seconds
7.9 inches per second
***better than 25% improvement - this is possibly the limit of the stock motor

*the amount of work for regearing compared to a motor change may not be worth the effort *unless* we have to stay with the stock motor (which may be the case for the Disneyland model).

Tamiya Torque Tuned Motor (with brushes from original motor), stock gearing
less than 750 mA (runtime > 2 hours)
13 seconds
about 11 inches per second
***almost double the original speed

Tamiya Torque Tuned Motor plus regeared*
750 mA (runtime ~ 2 hours)
9.5 seconds
14.7 inches per second
***more than double the original speed
0.493" drive wheel, 90.3 rev per lap
approx 8550 motor rpm

Note that the rpm is much lower than the rated rpm of the Torque-Tuned motor, 16,400 at 2.4 volts. No load rpm is almost meaningless, the maximum power is often at about half that figure.

The test shows the original monorail motor runs near it's peak efficiency, it is highly likely the designers selected the gearing to do just that. My regeared monorail showed about a 20% increase in speed but at a 20% increase in power. The motor is now running past it's efficiency peak and any further increase in speed will take an even greater increase in power. The designers probably found the diminishing returns to be not worth the reduced battery and motor life.

*More on gearing: I modified the gearbox to accept two new gears that change the overall ratio from the motor to the drive wheels.  The ratio is changed from a total of about 26:1 to 15:1. Although that is a 75% increase the motor will not power that much of an increase, I suspect we can get at least a 25% improvement before the motor is overstressed. Because the motor is operating well off the efficiency peak there could be a greater than 25% drop in battery life.

Later: The original motor could not take full advantage of the regearing, the rpm dropped too much and it was out of it's efficiency range. Still, a 25+% improvement with no other changes is pretty good. The Torque Tuned motor did better than I expected, it really matches the new gearing and shows a dramatic speed increase (as well as a similar current increase). I may try a Rev-Tuned motor but with the original gearing.

Further improvements: The monorail's rollers are designed for low cost with plastic rollers and no bearings.  The top beam rollers are too small for good operation.  The side rollers have that odd tapered shape that has the smaller bottom of the roller going a different speed than the top, fighting each other and causing drag.  The drive rollers on the powered cab have the same problem but made worse by the rubber roller on the left side.

***February 2016

WhisperJet Drive - the belt drive system is not as efficient as gears but the drive wheel on top of the beam is more efficient than the original drive system. WJ runs a circle in about 10 seconds with a current draw of 1.25 A so it is more than 2X as fast as the original but takes about 3X as much battery power. *The real benefit is that this one is *quiet*.

PN Racing motor

1250 mA (runtime ~ 1-1/2 hours) (neo magnets reduces current to 950 mA)
10 seconds around the circle
14 inches per second
~ 10:1 "gear" ratio
0.610" drive wheel, 73 rev per lap
approx 4380 motor rpm

With a reduction ratio of 10:1 the motor is running at a slow speed compared to the others, which helps to reduce noise. The motor is probably well out of it's efficiency range which shows up in the current draw but it performs well. The stronger Neo magnets reduce the current considerably.

***Update March 2016: a set of neodymium magnets reduced current draw to 950 mA with no effect on speed! Adjusting the overall reduction ratio to about 16:1 further reduced current draw with very little change in speed.

As a design exercise I built a new drive system for the monorail with gearing that is about 5x faster than the original.  The monorail kept leaning around the curves until it finally ran off the beam.  There is a limit!

Btw, 12" per second is about 60 mph (in HO scale), perhaps slower than the real monorail can go but faster than it is allowed to go.