From what I could determine, there is no fixed ratio, but PRR's number is an excellent starting point. And yes the cathode resistor is an important design consideration. With tweeking, the ratio can get closer to 1.
The power ratio number you seek is:
P = 1/2(1 + i22/i12)
where the self-split power is proportional to i12 + i22
and the conventional PP is proportional to 2i12
I enjoy the questions and issues you raise in your posts and threads. I quoted an article found in Wireless Engineer by Amos dated February 1946, With the Title "Push-Pull Analysis, Subtitled "Cathode-Coupled Output Stage".
From this article, I make the following recommendations to you.
1. If you choose to use self split output;
a. Use pentode tubes, you will have a greater output.
b. Familarize your self with the design aspects, Like any tube design, there are unlimited choices of components, and the inter-relationship between component choices. My guess, would be to put together a spread sheet and model the impact of the choices.
c. Put together a library of resources. This includes the article mentioned above, and copies of the two patents mentioned in the article. (#492,407 and #508,697) I would recommend another ariticle: Compact Hi-FI power amplifier by melvin liebowitz/ Delaware Electronics Supply Co. subtitled "Constructing a 6-watt amplifier in which the output tubes serve as their own phase inverter. power tubes are EL84's. This article is no where as detailed as the Amos article.
Determination of the i's is circuit dependent, particularly the value of the cathode resistors.
I left a lot out, and this post is long enough.