VFDs work well for single machines but not well for things like CNC that may contain their own VFDs on one or more axes, or things like welders that may have significant instantaneous loads. VFDs also do not work well if you are interested in "plugging", ie throwing the motor into reverse to rapidly stop it or back out.
That doesn't work well since L1-L2 are 180 degrees out of phase not 120 and the phantom phase will be way out of proper sequence.
Never ran one of these, have you? You put in single phase on L1-L2 and you get the other two phases generated on L1-L3 and L2-L3. They are not perfect, but you can tune them a bit with run caps. It works well enough to be able to run CNC equipment and anything that uses 3ph motors. There's enough energy stored in the rotating mass to be able to handle some peak starting currents, but it's important that the idler not be too small for the load.
If I had unlimited money, I'd get a Phase Perfect which essentially synthesizes 3ph power and is built to handle machine shop loads. Rotaries are cheap and work well enough for most cases though.
Back to the original problem: gear your pony down so it can get the idler moving. If it's moving fast enough it will pull into synchronous speed when power is applied. You might have to decouple the pony then. One thing to try is to have a loose belt between the pony and idler and use a lever to pull the pony tighter to the belt. Start the pony, apply tension and let the belt slip until the idler is up to speed then apply power. Not elegant, but will work. Just don't get caught in the belt. You need to get the pony to speed and then have some kind of slipping clutch to get the big motor up to speed.
You could wind a rope around the motor shaft and give it a good pull which would probably work. Be sure the rope is clear before applying power
Edit: Here's a thought. Get a 1hp 3ph motor and a small VFD. Use the VFD to drive the small motor. Couple the motors then you can ramp up the VFD until the idler is at synchronous speed. Depending on the mass of your idler, you may still need to gear things down a bit, but you can program the ramp time on the VFD and it might just work fine.