Here is a wing planform where Schrenk will predict zero lift at the tip.That seems correct. Since the "Schrenk line" is an average of elliptical lift and planform lift, if the planform were elliptical both the planform line and elliptical line would be, well, elliptical. Therefore the average of the two identical lines would be the same identical line. The only way the schrenk line will go to zero at the tip is if the planform goes to zero at the tip, such as the elliptical planform or the unlikely case of a wing that tapered to a point at the tip.
Not the best way to increase effective aspect ratio as the tip vortex is looking for an edge out at the tip to attach to. This one will attach somewhere between the tip and the aileron edge.