The Wireless World Monodial is now working again. I've not checked the alignment, but it pulls in LW and MW stations just fine. The silent tuning feature works, but probably doesn't justify the extra cost then (or now). The tuning indicator isn't right. The resistor controlling it had been changed, maybe my replacing the weak vari-mu pentode affected things. More investigation required when I do the alignment. But first I need to order parts to build a suitable amplifier.
I'm thinking of using a 1940s pentode, e.g. KT61 rather than a 1930s type.