Ltk--"The problem, I think, is that the RPC does not have a contactor on the output side at all, and for a $2,200 unit that is absolutely ridiculous. As far as installing one myself I have no idea where to begin or what to buy?"
You are correct about this being one solution. With all the discussion which has occurred, there has been little specific to where you begin, what to buy, or how to install it.
The below is what I would do in your situation. I am not going to claim it is the only way, or even the best way. It is a simple practical approach. I will make links to representative products, but intend them as examples, not an endorsement of brand, size or price.
I anticipate others will have other suggestions and corrections if needed.
You will need a 60 amp 3 pole contactor with a 240 volt coil, A time delay relay rated for 240 volts, a way to fuse the two control lines, some conduit and fittings, and a NEMA 1 enclosure with inner panel. The enclosure needs to be large enough to contain the 3 pole contactor, time delay relay, and room for wires to bend- and for you to work in. If in doubt, get one bigger.
What you will be doing is using the L1 and L2 connections to the idler (A and B in the factory diagram) to power the coil on a 3 pole contactor. The contactor control wires go through a time delay relay located in the breaker box before the contactor coil. L1,L2 and L3 from the RPC to the breaker box now go first to the enclosure, connect to the 3 pole contactor, and then on to the breaker box.
The RPC is started and stopped though its usual control buttons. When the RPC contactor closes and powers the idler, it also provides the current to close the added 3 pole contactor, which then connects the RPC to the breaker panel. The time delay relay in the control wiring allows the RPC to fully start before any current goes to the breaker box and on to the machines. This also allows you to turn off the RPC before it connects to your breaker panel if it does not start as it should.
The use of 240 volts in a control circuit is for ease of construction. If the RPC has a transformer and a lower control voltage system you may be able to use that to control the added contactor. Not knowing if this can be done, the design is for what we know can be used.
Construction
Connect the control wires to L1 (A) and L2(B): It would be tempting to add the control wire to the existing terminal where the idler connects- but unless approved for it, there should be only one wire per terminal. It might be possible to wire in a power distribution block . If not, I would use two Polaris taps. The wires should be fused. If there is room you could wire in a fuse block. If not, use two in-line fuses.
The control wires between the RPC and the enclosure should be in their own conduit, with a separate section of conduit for L1, L2 and L3.
The enclosure will have an inner panel. The 3 pole contactor and timer are mounted on the inner panel, then the panel and components are mounted in the enclosure. The wires you have going to the breaker box will now go to the 3 pole contactor, then on to the breaker box.
Polaris tap:
NSI Industries Polaris Black IPL4-3A Insulated Multi-tap Connector - 3-Port Single-Sided Entry for 4-14 AWG Wire Range - Dry Locations - Dual-rated for cooper and/or aluminum - 1.188-inch width, 1.375-inch height, 1.55-inch length - Hex size 1/8-inch: Wire Terminals: Amazon.com: Industrial & Scientific
Time delay relay:
McMaster-Carr
Power distribution block:
https://www.mscdirect.com/product/details/84720432
In line fuse holder:
McMaster-Carr
Fuse block:
https://www.mscdirect.com/product/details/54002720
3 pole 60 amp contactor with 240 volt coil:
https://www.mscdirect.com/product/details/51532364