Aluminium chloride 20% in Beeler basis is not stable. Can a different creme base be used for this or is a lotion a better solution?

It is not surprising that the image base breaks. After all, AlCl3 reacts with lauryl sulfate and already forms lauryl sulfate, which is supposedly insoluble in water;  

Since I am not for 100% sure that it succeeds, you can best try on a small amount with cetomacrogol cream. If the cream does not break, there is the solution. However, if the cream Is unstable, you can better switch to a lotion, as described in the TMF;