Voltage regulators and input impedance

I have an Audio Research Ref 5SE pre running into a Modwright KWA 100SE power amp. The input impedance of the Modwright is listed as “15K at 50 Hz” and the specs on the Ref 5 suggest “20K ohms minimum load”. 
 

So here is my question: I have gone through 3 6550 tubes in the Ref 5 (which AR says is used as a “voltage regulator” in the power supply) in the past 3 years - sovtek, tung sol, svetlana, all new. The last one lasted under 500 hours. I am thinking of potential causes, including excessive heat (the location needs better ventilation), something wrong with the preamp, etc, but I am wondering about that input impedance on the power amp. Am I running the Ref 5 into too little of a load? Would that put undue strain on the power supply tube, causing it to fail prematurely? Would love to hear from someone who knows this stuff better than I…