Update to my last post: the Timberland Boot Kit helped a bit, with a few cycles of brushing and cleaner and then conditioner. But what ultimately helped most was dried bread. :
Timberland Boot Cleaning Tutorial - YouTube
Timberland - Accessories - Boot Kit - Nohble
Amazon.com: Timberland Travel Kit Plus Shoe Care Product, no Color, OS 0X US : Clothing, Shoes & Jewelry
Timberland Product Care Travel Kit | Journeys
Product Care Travel/Gift Kit | Timberland US Store
Amazon.com: Timberland Boot Kit Shoe Care Product Set, No No Color, One Size Regular US : Clothing, Shoes & Jewelry