Joshua,
Jeff from over at OWWM. A few thoughts about what has already been suggested. Woodhick (another OWWMer) says he starts his 7 1/2 HP 24" planer with a 10 HP idler and that start-up is 3-4 seconds. As you know I have a couple of 20" planers. Both have Baldor 7 1/2 HP motors. Whether I start the one I'm running with the 15 HP side of my RPC or with both (22 1/2 HP) of idler running, my start up times are on the order of 1 second or less. I can't discern any difference from equivalent planers wired to utility 3 phase. Woodhick starts his feed motor, after the c-head motor. Due to needing to rework my reversing drum, I start my feed motor first, actually it starts when I energize the 3 phase output of the RPC if the planer is plugged in. Though my cutterhead weighs about 25% more than yours (I didn't do the rotational inertia calculations), your 180 has to get more started when you consider the feed mechanism. A proposed experiment: Have you timed starting your planer with the feed speed at the lowest and highest rates? It wouldn't suprise me if the added mechanical advantage of the slowest speed would decrease start times a hair. Not a solution.
As gpkull stated "use the saw as an idler untill the planer comes up to rpms". I can't recall your setup but if you have the outlets and the ampacity it would be a cheap way to a 17 1/2 HP idler. Measure your voltages (for balance) and currents (for capacity) with the RPC and saw running. See if you have the amps to spare. Remember, with the RPC and saw running, the planer will not pull near as many amps at startup.
As Toolnut (yet another OWWMer) said, you might try balancing to a higher voltage to eliminate some of the inevitable sag.
Lastly, and perhaps the better solution, what YoungDen suggested; wiring in a start capacitor circuit at the load motor. Before trying this I would look at your wire sizing and do the math remembering you are not going to be dealing with a balanced 3 phase load (at start up) nor a single phase load (FLA X 1.73). Probably somewhere in between, perhaps Peter or Jim would know. My 221's came from Powermatic with 10 gauge to the mag starter, 10 gauge from starter to cutterhead motor, 12 gauge for the feed-motor circuitry (drum and motor) and 12 gauge for the remote on/off station. I am going to upgrade the run from the 3 phase distribution to machine to 8 gauge.
Now, how to engage/disengage the start caps? I thought of 4 ways:
1) a seperate HP rated switch controling the start caps or a smaller switch controling a contactor. Would work but not elegant.
2) utilizing the NO switch from the three wire control station to energize a contactor as long as it was depressed ..... hold it down until the machine was up to speed. I can't off the top of my head remember exactly how a 160 or 180 is wired. The contactor for the caps would not have a regenerating shunt to keep the coil energized, the mag starter would need the shunt as it's wired now. I can't see how to seperate them and operate with the same switch. Maybe Jim, Peter or Toolnut know a way???
3) Using a potential relay such as a Grainger (GE) 6X550 or SteveCo 90-66 to drop the caps out when the motor is up to speed. The problem is the relay monitors the voltage between one of the utility legs and the generated leg. Fine for starting a 3 phase on single phase where Vo in the generated leg is zero, not so good when Vo in the monitored phase (utility<->generated) is around 240 V., above the drop-out. The voltage may sag enough during start-up to energize the relay but I doubt it.
4) an adjustable timed relay. Ray Muno uses a timed relay to start his RPC as do several of the guys here at PM. They could probably steer you towards a good unit.
Lastly, if you built and balanced your RPC as per Fitch Williams, you should have approximately 60% of your run between one of the utility legs and the generated leg. Parallel to this are your start caps, eh? If you do try to use additional start capacitance to kick start the load motor, make damn sure that the capacitors or between those same two legs.
My $0.02
Jeff