I'm sure resistive losses play a role, but I'm also pretty sure, considering the numbers, that the real reason is to have a sufficient number of secondary turns so that there are complete secondary layers to interleave with the primary winding; thus maximising mutual coupling.
Now I have a plan. I've decided that I'm going to rewind the transformers for a lower primary impedance, of 8k instead of 10k. This will yield a slightly higher power output from the amplifier, but still within the capacity of the power supply. As the primary impedance is raised, it becomes exponentially more difficult to keep a limit on things such as leakage inductance and winding capacitance and thus achieving and adequate high frequency bandwidth.
8k versus 10k may not sound like much, but it makes things quite a bit easier overall. Secondly, I will not aim for a stupidly high primary winding inductance - for the reasons already adequately detailed. For the interleaving, I will use the supposedly established standard of 5 primary sections and 4 secondary sections. I will use the parallel winding method for the secondary to maximise mutual coupling with an adequate number of turns. I'm also going to retain the pentode configuration of my power output stage, with the fixed DC potential on the screens, so I will not be be incorporating Ultra-Linear taps into the primary winding, as they thefore have no purpose.
I will initially wind a primary inductance of 100H. The only real, vaguely questimated variable at the moment is how well this plan will juggle the ratio of leakage inductance to the primary winding capacitance. It is these two elements that determine the HF roll-off of the transformer. The leakage inductance forms a 2-pole (12 dB per octave) low pass filter with the winding capacitance. For optimal squarewave/ step response, you don't want this filter response to have an excessively high Q and thus overshoot/ringing. You don't want it to be overly damped either. A Q of 0.71 (Butterworth) would be ideal (as Mr Beijner mentions in his paper), but IMO anything in the range of 0.5 to 0.71 would be perfectly OK.
I may very well end up winding and scrapping a few iterations before I wind up with a transformer that I am happy with. I'm going to resort to a little carpentry and metal turning to knock up a hand cranked winding jig that supports both the bobbin and the wire spool. I have a plan in my head that will be pretty simple to make. So far I have raided my junk box and come up with a pair of these (lovely vintage

) "Silver King" mechanical counters (see attached), that advance one count for each full turn of the input shaft - perfect for counting wound turns! I also have a nice stash of high temp yellow transformer tape that I use for my SMPS ETD's.
Also before I can start calculating required turns and winding my transformer I'm going to have to workout the Al value of the core as I really have no idea who makes it and don't have the original manufacturers data. I think the easiest way to do this will be to wind a full layer of (counted) turns onto the bobbin, reassemble with the E-I's and accurately measure the inductance. Knowing both the number of turns and the inductance value I'll then be able to compute the Al value.
However all this will have to wait until next weekend before I can get started. Maybe some out there find all this interesting, I dunnno.