Hi Slag
I actually think that your attempt in trying to work out a rule of thumb is very laudable, and that you get some undeserved flak from people making assertions that they can not substantiate.
Though the efficiency of the prop gets vastly better with speed, the thrust does not.
How is that then?
Certainly most fixed pitch props are not efficient at the low speed end as they will be optimised for cruise conditions. And how about the power output of the engine. Again fixed pitched props do not allow the engine to put out the rated power and as you accelerate and the prop becomes unstalled and more efficient you will see that the rpm increases thereby allowing the engine to put out more power.
It is unlikely that the acceleration of the typical GA mount is constant. But never had the impression that it decreases during the take off run either as bookworm states.
Of course you need to consult POH and factor in the various parameters before you attempt your t/o. But to do a real life check whilst trundling along seems a clever plan.
As always, MHO
FD