Welcome to the forums!! Very interesting - Could you explain a bit more about how you are doing the experiment? How exactly are you accomplishing the radius increases, is anything else changing?
(I've never actually considered the effect of coil radius on efficiency, but I'm guessing it actually makes sense that it is getting more efficient. The core acts as a 'conduit' for magnetic flux, but you still have flux leakage out of the core. Making the coil larger at the other end actually means some of this 'leaking flux' manages to get captured by the coil and thus gets used to induce a voltage, rather than just being wasted. Think of it like trying to catch tennis balls - Yes, most of them are travelling where you want them (in the core), but some might get flung outside that path. A larger coil radius is like having a bigger net, more likely you'll catch em
)