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You might already have thought about many of these strategies and resources, but I thought I'd bring them up just in case they're useful.
The Related Resources page in the digital edition of Theodore Roosevelt's papers at the Library of Congress lists related manuscript collections in the Manuscript Division. The bibliography on this page also lists relevant secondary sources, including various published editions of Theodore Roosevelt's letters. The indexes to these published editions might be used to identify letters about subjects like the environment and conservation, and the citations in secondary sources can also lead to other relevant manuscript material.
The Theodore Roosevelt Papers themselves are generally arranged by record type and therein chronologically. You can use the finding aid for this collection in tandem with your background knowledge to identify potentially relevant points in the collection to search, and then click on the “digital content available” hyperlinks in the Container List section of the guide. Clicking on the hyperlink will forward that page to the object record for the material. A three-volume index to correspondence can also help pinpoint letters to or from specific people or groups.
In 2002, the Library also produced an online exhibition The Evolution of the Conservation Movement, 1850-1920, which documents the historical formation and cultural foundations of the movement. You can search this online exhibition by keyword to look for material related to Theodore Roosevelt.
All the best of luck on your research!