In case this isn't already common knowledge...
Triumph 3HW brake shoes seem to be hens teeth, other than the Indian copies, which are still not cheap.
So I ordered a pair of the cheap and cheerful, and easily available, Triumph 3TA/5TA front shoes for the 7" full width hub from the 1960's. I'm not so knowledgeable on Triumph stuff but do know that exactly the same hub and shoes were used on BSA B40, early A50 and '68 B25. I also know that around 1962 BSA changed from pivoted shoes to fully floating in the same hub without making any part changes to the hub or brakeplate. The floating shoes just sit and slide on the old fulcrum pin. On that basis, lets see if they will fit...
The shoes which arrived were 1/16" wider than the original 3HW shoes so were easily made to sit flat and straight against the inside of the brakeplate by linishing just over 1mm from that side of each shoe. Other than that they went straight in, the other side of the shoes left original size didn't bottom in the drum.
Maybe they will give a marginal improvement to the brake, which is why they replaced the pivoting shoes in the first place.
They are also handed leading and trailing, again to theoretically improve the brake, so need to be fitted with the unlined end of each shoe facing towards the oncoming rotation of the drum.
If and when required I'll treat the rear hub the same, no reason why they shouldn't adapt to fit and based on the precedent that the Victor GP used exactly these front floating shoes in the rear drum.