Ok, here's an update:
I ran the battery low by cranking over the second generator. For some reason, It wouldn't keep fuel prime. I ordered a Schumaker 24v battery charger off of Amazon and got a chance to crank the genset over yesterday. At first, I had the same priming issue, but after cranking and pumping with the manual fuel pump about a million times, it finally started! Boy, these things sure knock when you first get them started. Likely due to them being stored without oil and needing to get some fluid moving for the first time in years.
While it was running, it began to surge and the solenoid would randomly pop out. I was worried about this and spent some time investigating before I just got tired and held the solenoid back and manually manipulated the governer to keep the genset running. After about 2 minutes, I noticed that the surging stopped, and after about 4-5 minutes, the solenoid stopped firing. Not sure why this was happening (though I have theories), but it worked itself out in a matter of minutes. The set also stopped knocking and started running more smoothly.
One thing I noticed is that the return fuel lines (the small braided one) on both gensets are wet and weeping fuel slowly. This is not surprising, and I ordered a couple of meters from mercedessource.com (look for the braided fuel return line for the W123 Diesel) as a replacement.