I am getting deeply confused by all this. Though I normally deal with IEC-frame motors, pretty much all of the general principles seem to apply to 3-phase motors in general.
I concede it is just about possible that you are all talking about 56-frame motors, and that the technicalities of getting a couple of HP out of a motor frame that was originally intended for Fractional Horse Power motors mean that they are wildly different to other, industrial, motors: sticking with the 56 frame size obviously removes the option of going up a frame size when dropping a speed to maintain the motor output. The reason I'll talk about "most" motors is because I do not see enough 56-frame motors with high outputs to know whether they are a special case.
I've been using VFDs on and off since the mid 1980s. The advice given by both motor and VFD suppliers for most of that time has been to use a 4-pole motor and vary the speed between 10 Hz and 100 Hz when the speed turndown range is important.
The mechanical components of (almost) all motors are standardized as far as practicable; the difference between a 2-pole, a 4-pole and a 6-pole motor of the same frame size will just be the windings and these are static. The rotor, bearings and seals will be the same on the 3600 RPM, 1800 RPM and the 1200 RPM variants. If the manufacturer offers variants with higher pole counts, these will also have the same rotating components. It's just the way modern manufacturing works.
This means that the moving parts of an 1800 RPM motor are exactly the same as the moving parts of the 3600 RPM variant and therefore are safe to run at the same speed.
As a general rule, motors tend to be designed to run on both 50 Hz mains supplies and 60 Hz mains supplies, even if the rating plate only mentions one of them. As frequencies get further from the 50-60 Hz design range, losses tend to increase within the motor and efficiency drops. Back in the mid-'80s, the advice was that 10-100 Hz caused no problems, but things tailed off quite rapidly once you left that range. That was close to 30 years ago (ancient history; nobody had a mobile phone!) and things seem to have improved over that time. Certainly I see no problem at all when running a current model industrial 4-pole motor to 120 Hz. I don't actually see a problem when I run at 150 Hz either, but I prefer not to exceed the mechanical design speed of 3600 RPM. So far, I have been unable to find a manufacturers statement that gives a permissible speed in excess of 3600 RPM when run on a VFD (with the exception of 400 Hz, 24000 RPM spindle motors and other specialist stuff).
On basic V/Hz drives, the lowest frequency I am comfortable running is 10 Hz. It does not seem to matter whether I am running a 2-pole or a 4-pole motor, I find that somewhere between 10 Hz and 7 Hz, it starts to feel "coggy". It is enough to affect the finish on my lathe (my normal test-bed when playing with a drive for the first time), but I don't know whether it would be as noticeable on a belt grinder. A V/Hz drive has a fixed (usually) linear relationship between Voltage and Frequency when running below the rated frequency.
In line with the manufacturers claims, I find that "Sensorless Vector" drives provide better low speed performance, running smoothly down to a couple of Hz or less. SV drives incorporate some additional circuitry that measures the motor power factor and adjusts the Voltage on-the-fly to hold the power factor within spec. Although SV has been around a good few years, I don't think the most popular of the sealed drives (Nema 4/4X, IP55-IP66) offer SV capability. The sealing is obviously more important than SV with metal dust about. At higher speeds, I cannot discern any real advantage with SV drives.
If you are limited at the bottom end of the speed range by the loss of smoothness at, or just below, 10 Hz, and at the top of the speed range by the motor designers maximum design speed of 3600 RPM. a 2-pole motor will give 10-60 Hz for 600-3600 RPM, a 6:1 turndown. A 4-pole motor will give 10-120 Hz for 300-3600 RPM, a 12:1 turndown.
It looks like the 4-pole has the advantage.
Because of the way that VFDs work, the speed vs power delivery profile of a 2-pole motor is different to that of a 4-pole.
Below the motor rated Frequency and Voltage, the VFD varies the Voltage supplied to the motor linearly with the frequency. This means that the motor operates in "Constant Torque" mode up to the rated speed. The Torque is directly related to the current, with the rated torque being developed when the rated current is drawn. Once the rated frequency and Voltage are reached, the drive can keep increasing the frequency, but the Voltage must be kept at the rated value. Above the rated frequency, the motor runs in "constant power" mode.
Power is Current times Voltage. The maximum current is whatever the rating plate says. For a 220V 3-phase 2 HP motor, between 6 & 7 Amps seems fairly typical.
If we take a 2 HP, 220V 2-pole (3600 RPM) motor and a 2 HP, 220V 4-pole (1800 RPM) motor and compare power outputs at various speeds:
At 300 RPM, the 4-pole motor is operating at 10 Hz and 37 V (10/60ths of 220V) and will generate 1/3 HP
At 600 RPM, the 4-pole motor is operating at 20 Hz and 73 V, to give 2/3 HP
At 600 RPM, the 2-pole motor is operating at 10 Hz and 37 V, to give 1/3 HP
At 1200 RPM, the 4-pole motor is operating at 40 Hz and 147 V, to give 1 1/3 HP
At 1200 RPM, the 2-pole motor is operating at 20 Hz and 74 V, to give 2/3 HP
At 1800 RPM, the 4-pole motor is operating at 60 Hz and 220 V, to give 2 HP
At 1800 RPM, the 2-pole motor is operating at 30 Hz and 110 V, to give 1 HP
At 2400 RPM, the 4-pole motor is operating at 80 Hz and 220 V, to give 2 HP
At 2400 RPM, the 2-pole motor is operating at 40 Hz and 147 V, to give 1 1/3 HP
At 3000 RPM, the 4-pole motor is operating at 100 Hz and 220 V, to give 2 HP
At 3000 RPM, the 2-pole motor is operating at 50 Hz and 183 V, to give 1 2/3 HP
At 3600 RPM, the 4-pole motor is operating at 120 Hz and 220 V, to give 2 HP
At 3600 RPM, the 2-pole motor is operating at 60 Hz and 220 V, to give 2 HP
At all speeds below 3600 motor RPM, the 4-pole motor seems to have the advantage.
Because power is Torque times RPM, generating the same power at half the speed requires double the torque. Usually, this means that the 4-pole motor of a given power is physically bigger than the 2-pole motor of the same power in order to supply the increased torque.
In the special case where a machine is designed around a specific motor frame size, going to a 4-pole motor might not be realistic, but in most cases, the 4-pole motor is the best fit to a VFD-equipped machine.
If your motor has ratings for both 50 Hz and 60 Hz, it can often be worth doing the sums for both sets of figures, as one will often give more area under the curve than the other. It's not always the 60 Hz values that are "better", nor is it always the 50 Hz values.