OK, lots of questions.
TUNING
First thing with my designs are that everything I build is CNC rated. Meaning less than 5% voltage difference leg to leg.
Does it matter for older contactor/ switch controlled equipment with one or two basic motors and no electronics, it does NOT matter a lot as long as you are no over 10 % leg to leg different. For CNC gear, gear with electronic controls and the like it's very important.
.
If you have too little run capacitance, you will typically have low voltage, which means that you will also have low current. Yes, current does the work but voltage is the potential to DO work. If voltage decreases then so does current. Second, TOO much capacitance. This will generate higher voltages on the generated leg and will typically cause even more problems than too little voltage. And you can get the voltage on the generated very high on the generated leg if you get way overboard. I have seen 350 volts on a 3rd leg a couple times. That WILL fry things.
An RPC is a tuned circuit of sorts. ANd do to that getting it tuned right is important.
First reason it's important is that it will draw the least amount of current while idling. This means lower electric bills for you or whoever is paying them
Second is that a properly tuned RPC will start a motor at least twice it's size when that motor is not under load. I have spun up 40 HP motors testing them with a 15HP RPC. Mind you the motor was bare and sitting on the shop floor but it started the same as it did when I got it and tested it on the sellers 3 phase power in their building.
Now, the actual tuning part, or HOW TO TUNE an RPC
First part is that you DO need to use run capacitors between L1 and L3 and L2 and L3. The 9 to 15uF per horsepower of te motor is about right.
But tuning can be tricky. First thing to know is to move up and down slowly. Don't make 10uF jumps. I typically will have the figured amount of capacitance in the circuit and then have 3 additional capacitors for tuning. two are 5 uF and one is a 10 uF. Here is an important thing on capacitors. Wiring them in parallel increases the total value of capacitance, while connecting them in series decreases the total value. Two 5uF caps in parallel is 10 uF while 2 in series is 2.5uF. So base tuning can be done in 2.5uF steps from 2.5 uF to 20uF with only 3 capacitors.
First voltage to look at is the L1 to L2 voltage. This one will typically not vary as it's line fed and would require excessive current draw to get it to decrease. That is the voltage you are working to obtain for both the L1 to L3 reading and the L2 to L3 reading. Start with the L1 to L3 and adjust the capacitor value until the voltage matches the L1 to L2 voltage. Turn the unit off every time before adjusting the capacitor values. Once L1 to L3 is adjusted, work on the L2 to L3 voltage. Again, power down before changing out the caps. Once it's right, go back and check the L1 to L3 voltage. Changes are it moved up or down. Again, attempt to adjust your values to get it back to where it was matching the L1 to L2 voltage. YOU WILL NOT TYPICALLY GET ALL THREE READINGS TO PERFECTLY MATCH. Not possible so don't beat yourself up over it. So you are working for close as possible. After you go back and forward twice with it that's typically gonna be it.
START caps
25uF to 50 uF per horsepower and sometimes as much as 100uF per horsepower.
Your motor should take about 2 seconds to start. Anything more than that and you are just killing the capacitors and the motor. Remember that START caps are not run caps and can't remain connected to the motor after it's started. They will overheat and blow up.
Something else on RPC design. Install a contactor disconnection the output while the start capacitors are in the circuit. Reason is simple.
Remember where I said that too much capacitance will increase the 3rd leg voltages drastically. Well the run capacitors are about 9 to 15 uf per horsepower but the start capacitors are about 25 to 50 uF per horsepower. Guess what happens to the 3rd leg voltage during startup? If your RPC is connected to any device that has a constant connection to the input voltage, like a power supply to run the control circuits, it's gonna get that 300 or better volts put across it. Guess what happens to a device designed for 240 volts when you apply 350 volts to it. The magic smoke leaks out and it stops working. So output contactor is important.