Marty,
Cousin P here. I have news of the Strood Union Workhouse from Medway Records. Alas it is little help. Grand-Father was placed here by a Mrs Elliot (not Frederick William). Not sure if Herbert was admitted at the same time.
I have posted the Boy's Home in St Peters, Westminster to see if I can obtain a copy of Reginald's entry into here. Seems he checked in and out of Farningham Little Boys Home in Sept 14 but was re-admitted in Nov 14, then was placed with an American Repair Co in Edgeware Rd (you probably have this info, nonetheless, it may assist.
Regards