Are you able to answer the above question highlighted in red?
So you started by the bold and earth shattering claim of "it doesn't account for the vapor carried out by the bubbles directly produced by boiling!", which would be devastating to all of F&P's work.
May be you did not understand the ramification of your claim?
You mean you tried to read the 1992 paper again and did not understand it?
Or tried to read the seminal 1990 paper and did not understand where the term for vapor is included?
What about reading the Wilson critique from 1992. He explains the terms well
Or while you are at it you could also read the Fleischmann reply to Wilson, where F&P explains further the calorimeter enthalpy balance
Or just take a course in Electrochemical calorimetry