Using forward voltage drop of diodes with linear regulator
Using an op-amp is probably the best way to deal with this requirement but you might be better with an emitter follower circuit: -



The op-amp will drive the NPN so that its emitter (Voltage across the load) is the same voltage as the +Vin pin on the op-amp.

I borrowed "The Photon's" drawing because although it was wrong, it was easily amended to show an emitter follower. If you did use a FET (N channel with source to load) this would work but you might find that Vin needs to be higher for it to work. BJT base drive only needs to be 0.6V above the emitter - I'd still recommend using an op-amp with rail-to-rail output capability so that Vin can be a bit lower.

I'm also assuming the op-amp is powered from Vin and GND.