The good conductivity of Al alloys is not a part of the problem. Both copper and silver have better conductivity and can be silver soldered with ease. The process of silver soldering relies on the production of a range of alloys in the joint – with eg a copper to silver joint: copper at one side, various versions of bronze in between, changing to various silver alloys, then silver itself. If any of the resulting alloys is weak, or has a tendency to crack, absorb gases, etc, or has too low a melting point, then the joint will fail.
This means that some metals just won't work in this way. One example I have found is gold (which itself comes in a wide range of alloys). Trying to solder gold using silver solder can, sometimes, result in a molten puddle as one of the intermediate alloys has a much lower melting point. With Aluminium having a melting point not much different from most silver solders, along with its tendency to form crusts of oxide which do not dissolve in flux, means that joints in aluminium alloys are not really possible with silver solders. Not in ordinary workshop conditions, anyway.
Sorry.
Cheers, Tim