Here are some detailed datasheets for the two tube types if you'd like to compare. I haven't studied the differences closely yet, myself, so I can't comment on whether or not the 5965 would work
well in the One-Bottle.
12AV7
5965
(Datasheets courtesy of the magnificent "Frank's Tube Pages").
Just glancing at the datasheets and the plate curves, the tubes are obviously not the same but the curves are not
terribly dissimilar. The "typical operating conditions" given in that chart linked above are not really useful for comparing these tube types because they're not identical conditions! For instance, the conditions for the AV7 are given at 18mA plate current, but only about 8mA for the 5965. Of COURSE the plate resistance for the AV7 comes out lower, the Gm higher. You really have to look at the datasheets and the curves.
Really, if a 5965 is all you have handy, it's close enough to try out--you won't blow anything up. If you don't like the results, find a 12AV7. Simple...
The slight difference in max ratings for plate dissipation is not really a concern because the One-Bottle isn't working near the max rating of either type. (Tamas, the Ia column on that chart refers to the plate current at which those "typical operating conditions" are given, not the design-center maximums).
David, the input transformer you have is fine for either circuit, but the 1:1 output transformer isn't. The One-Bottle requires a 4:1 output xfmr; "Line Amp E" can use a 2:1 or higher ratio output xfmr.
Your power transformer will work (with a voltage doubler) for the One-Bottle, but its rated current is too low for "Line Amp E."
You mentioned something in your PM about using the preamp as a DI. Here are some input/output options for the One-Bottle that I posted earlier. They would also work for "Line Amp E."
PDF