The Carnot theorem likely evolved after Otto since this brought the compression cycle to the forefront of engine design. However, this relationship may have been made by Emile Clapeyron when reviewing Carnot's work. Few know of this guy, but at least wiki has this right...
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Last night, I read the whole thread on that other science forum where Tom continues his typical bashing. Oddly, someone mentions that the Carnot limit can be derived from the ideal gas law, but no one followed this up, instead diverting to the Clausius mumbo-jumbo. My spin is that the Carnot limit relates only to simple compression cycles where everything reduces to simple ratios. Moving away from these simple cycles may cost Carnot his crown, but I wouldn't waste much time chasing this.
BTW Fool, you made an error somewhere recently relating isothermal compression where you thought buffer pressure effected the heat of compression. Nope...during an isothermal expansion, the gas doesn't care where Wpos goes, so if more work goes to ambient vs man, no problem with heat/energy balance. Likewise, during an isothermal compression, the gas doesn't care where Wneg comes from, no problem with heat/energy balance. The simple 'proof' is that U=0 for any isothermal process, so the ratio of useful vs useless work per process doesn't effect Qin during expansion or Qout during compression. However, I know exactly what you're getting at and I posted it last year...that in reality, depending upon design, we pay Carnot on the front end during expansion or on the back end during compression.
Here's what you were wrestling with...consider 300-600k Stirling cycle where Carnot=.50 and we know that compression will be 50% of expansion...in a vacuum (no buffer pressure). So, if we consider Wpos=100 then Wneg=50 and Wnet=50. However, if a buffer pressure is present, then our Wnet=50 is reduced during the expansion process. On a cyclic basis, this changes nothing, but if Wneg>Wpos during expansion then the engine will stall before it ever gets the "free lunch" from ambient compression later in the cycle. This is what Senft gamed, but this obscures the fact that any LTD with a relatively high backwork ratio (and low thermal ratio vs this 300-600k example) has virtually Wnet=0
As you also said somewhere recently, using ratio simplifies stuff since ratios can cross-cancel integrals (when done prudently).