If you have a Steelhead-

Love your post! One has to remember manufacturers use tubes that will be reliable in the long term, not so much for sound quality. No owner of tube equipment wants early or unexpected tube failures but these can and do exist and if it’s under warranty, they want readily available tubes. 
Most tube equipment manufacturers encourage tube rolling but at the customers expense for good reason.

Have fun!

The 7044s, or any of the several congeners of the 7044, in the Steelhead are not "rectifiers", first because 7044s are dual triodes, not rectifiers, and then because they serve as White Cathode Followers in the Steelhead, which is just a fancy cathode follower. Cathode followers convert voltage to current while dramatically reducing output impedance and adding no gain to the signal. (Which is why it makes little sense to sub the stock tubes with very expensive equivalents.) The low output impedance of the cathode follower then makes it possible to drive either the volume control in the Steelhead, if it is being used as a full function preamplifier, or the outboard linestage, if the Steelhead is used as a phono only stage. In the case where you are using it as a full function preamplifier, there is a cathode follower that drives the volume control and then a second identical cathode follower that is driven by the volume control and outputs to the amplifier. So, the output stage sequence is: CF - (coupling capacitor) - volume control - CF - (coupling capacitor) - amplifier. That’s why, if memory serves, there are two 7044/6922s per channel, one for each White CF.

The 7DJ8 is by all accounts a nice tube, but bear in mind that it is designed for a 7V filament supply, not the 6.3V supply that is standard for filaments of most dual triodes and which is present in the Steelhead. Fortunately, it works on 6.3V, apparently.

For the single amplification tube per channel in my Steelhead, I substituted some Siemens CCa, happily, but I won’t say it’s a night and day difference from OEM tubes. I made some changes to the output section I described above, in terms of the output coupling capacitors, that made a much bigger improvement in SQ. Note that the signal must flow through two coupling capacitors on its way out to the amplifier, if you use the Steelhead as a preamplifier.

Lewm, thank goodness I did not post about Covid and Peter Lederman. Thank you for your elucidating post.
And, I do not use my Steelhead as a preamp. See my second post. Or not.

I used 7DJ8s in my Herron preamp and enjoyed the exact same benefits as you. I would suggest buying multiple sets as they didn’t last more than 18 months in that application. Totally worth it though. Love your gear!

Just out of curiosity, in the Herron what tube type does the 7DJ8 replace?