I finally picked up a 6X4 rectifier tube today. I was planning on building an adapter to use this tube in place of the 6Z4, but they didn't have any 7-pin sockets there. Since I really want to try this much better tube today I've decided to just modify the socket pins on the PS board itself. This mod is pretty easy since the two pins that need to be swapped are in the perfect place to do so. The only thing that I'm worried about is that the heater in the 6X4 draws 600mA which is right at the limit of what the heater winding is rated for. Hopefully the transformer can handle it.
I'll post my listening impressions later on tonight when I get it done.