Link took a bit finding! It is worth the effort to read this, honestly
(well it was for me; you might already know everything!)
A look at single-supply operation and the need for additional components in each stage for appropriate signal-biasing.
Basically, with the 2 resistor PD the amp's PSRR goes to pot. Your PD is one amp removed from the real amp, but I think the principle's the same . Better to stabilise the voltage than to get it exactly 50% (there's an obvious disadvantage if the supply is a battery, however)
Thinking a bit more about your actual problem - I've seen full calculations for op-amps which include all the variables, not just R1 and R2 (ie, the non-ideal characteristics of the amp) - perhaps if you can track this information down and re-calculate for each type of amp you will get results which match your experiments.
Or perhaps you are seeing effects of an experimental setup (eg, breadboard) which only affects the LM7322? Power and ground impedance, perhaps?
Would it be viable to use an output transistor (or totem pole) to get the current boost, instead?
Your circuit reminds me of one I created a while ago - the unclean offspring of a diff amp and a summing amp is approximately what I called it. Worked very well but needed 3 matched resistors!
It's a shame none of the experts are chipping in here... Guys? Gals? Heloooooeee....