Let's clear the air here with some factual information about speaker construction and reconing. I have done more than my fair share of both reconing as well as transducer development and testing.
1. Voice coils are available in a variety of nominal impedances, that's one of the variables involved in developing a driver for a particular application. These nominal impedances are just a rough average and there will be all kinds of variations based on the mechanical aspects of the driver and it's acoustic loading.
2. You can not recone a speaker without replacing ALL the moving parts. Once they are installed in a speaker, they are one with themselves and no longer come apart individually.
3. You will probably not be able to get an exact 4 ohm replacement that shares the same tuning as the 8 ohm version unless the OEM manufacturer can supply this to you (generally because they also use the different impedances in their other products)
4. There may be some available "close enough" parts that will get you going, but the tuning parameters may shift significantly. Enough that I would be concerned.
5. With the additional power into the speakers you describe, you will surely run way out of Xmax beyond 600 watts RMS. Also, power compression will rob much of the gain you hope to achieve. Maybe as much 50% of the gain.
6. With 600 watts into that single 15" driver, I would expect damage to occur over time. Micro-tearing of the spider fibers due to overexcursion is common under these conditions.
7. Even 600 watts RMS into the 210 would concern me... again at low frequencies the mechanical power handling of a cabinet falls of really fast.
8. Try your cabinets with the ShuttleMax 12.0 at 8 ohms per channel. You may find that the output is just fine because of the way the output tube emulation limiter works. There's a difference in how the limiter functions at 8 ohms versus 4 ohms, just like a tube output stage.