The ratings are continuous and intermittent. Just like many consumer products, the treadmill manufacturers have fallen to run-away ratings pressure. The continuous rating of the motor is the manufacturers rating at speed, current and voltage, under the thermal limit. However, since the treadmill only outputs high power when the foot hits it, they can claim a high rating for that instant (and if you are not to heavy and slow, then you don't trip the breaker, which happens because you cannot get 2.5hp for too long from a 1phase 120v 15 amp circuit). For much of the time the treadmill is running unloaded (in between your steps). If it is producing 0.25hp for 50% of the time and 2.5 hp for 50% of the time, then the rms value is about 1.8hp.
Here is what I would do.
Measure the resistance.
Take a power drill and back drive the motor, measure the voltage generated at speed (probably 500 rpm for a cordless drill) then convert this to what it would be at 1000 rpm. The torque constant can be calculated from the voltage constant. Take the amount of volts generated at 1000 rpm and multiply it by .085, the result is the torque constant in lb-in/amp.
With the rated current from the name plate and the above info you know almost everything about this motor.
Do not exceed an rms current of more than the continuous rating. And I would limit the peak current to about 2X the continuous (so the copper won't burn up). Keep in mind that if you are at 2X (that is 4X heating losses) you would not be able to do for long and still have the rms current equal the continuous value. Put enough voltage to overcome the would be generated voltage at the speed you want to run (stay within 2x the rated nameplate speed for mechanical reasons).
good luck, hope this helps.