You are completely ignoring the cost of cycling an aircraft, and that pretty graph is less than 10% spread from min to max efficiency. So no, you will not be better off landing.

Maximum efficiency merely indicates at which distance all parameters are matched most perfectly, it is not the distance above which one should land to take on more fuel to be more efficient.

Reduction to absurds is an easy way to prove that to yourself, imagine a flight of 3000 miles at maximum efficiency, and then one at 3001 miles at which you claim they should stop to take on more fuel. This clearly is not the case so there is something wrong with your statement.

Just to nitpick a little: The peak efficiency seems to be around 2500nm, and it's pretty flat between 2000 and 3000. Above 2500 nm, you have to compare to distance/2, since you compare between 1 and 2 legs. Example: compare the efficiency at 3000nm and 2*1500nm. The cutoff is slightly higher than 2500nm. But not far from 3000nm. Coincidentally London-NYC is 3000nm. So anything longer than that could be split off (if you don't take a detour to do so).