Why is the LT1054 circuit providing far more than double voltage?
First of all you should never measure the output of an unregulated supply without a load.  Try to choose a load that is close as possible to the final load you think the circuit will see.

From the datasheet for the LT1054, it appears the capacitor selection is rather critical.  In particular, under Capacitor Selection on page 8, it has specific recommendations for C\$_{IN}\$ and C\$_{OUT}\$. 

Ironically, in the schematic you copied from page 11 of the datasheet, C\$_{IN}\$ and C\$_{OUT}\$ are not labeled; but from the other examples it is clear that C\$_{IN}\$ is the 10 µF capacitor between CAP\$^+\$ and CAP\$^-\$, and C\$_{OUT}\$ is the 100 µF capacitor between V\$_{OUT}\$ and ground.

The datasheet first says that for unregulated circuits (like yours) the nominal values of C\$_{IN}\$ and C\$_{OUT}\$ should be equal.  Clearly their example schematic for a Bipolar Supply Doubler is going against their own recommendations.

Then they recommend using tantalum capacitors with low ESR values for both C\$_{IN}\$ and C\$_{OUT}\$

What I would do, is use a 10 µF tantalum cap, like this one, with an ESR of 0.3 Ω for C\$_{IN}\$ and C\$_{OUT}\$, and then optionally add a 100 µF electrolytic capacitor (which may have 10 times the ESR value of a tantalum) in parallel with the 10 µF tantalum for capacitor C\$_{OUT}\$.

If you have the parts, you might want to use the tantalum caps for the other two 10 µF shown in the circuit, on the left side of the chip, one connected to pin CAP\$^+\$ and the other to CAP\$^-\$.