What does the "20K ohms minimum load" tell me?Exactly what it says. Most ARC preamps are not recommended for amps with anything less than 30K but this one is good to 20Kohms. Your amps though have a 10K input impedance, which essentially means that the combination will be bass shy.
As others have pointed out, the output impedance of the LS28 **seems** sufficiently low, but that spec is done at 1KHz. At 20Hz, its output impedance is much higher owing to the size of the coupling caps at the output of the preamp. As a result, the 10K load of your amps will result in a bass rolloff.
So ARC is essentially telling you not to use this preamp with your amps.
We developed a direct-coupled output on our preamps so loads like the McCormick are no worries. At any rate, if you want to use a balanced tube preamp with your McCormick, ARC is not an option if you want it to sound right.